U2412M, HP Spectre laptop, connection

@Deb2020  Given that your Spectre has a USB-C port that supports video output, and that you have an unused DisplayPort input on your display, AND that any input other than ancient VGA will look noticeably better than VGA because VGA is analog whereas everything else is digital, your best option here is a USB-C to DisplayPort adapter/cable.  If you have to use a travel dock, maybe see if you can find one with a DisplayPort output.  Or since finding one with an HDMI output is much more common, is there any chance you can free up the display's DVI input that you're currently using with your PC?  If that PC has a DisplayPort output, use a DisplayPort cable to connect that PC to the display, and then you can use an HDMI to DVI cable to connect an HDMI-equipped travel dock to the display's DVI input.  (Note: Although DisplayPort to DVI and DisplayPort to HDMI cables exist, they are designed to connect a DisplayPort source to an HDMI/DVI input and cannot be used in the opposite direction, so that would not be a valid solution.)  But I'd really encourage you to get away from VGA, or at least relegate it to whichever system you use least, because it does look noticeably worse especially at 1920x1200, which is at the very top end of what VGA was ever able to handle.

As for the display quality issues you found, given that you mentioned "4K" in your Spectre model, I'm guessing that the resolution of the built-in display is 4K?  If so, it wouldn't make sense to duplicate a 4K display (3840x2160) to a U2412M (1920x1200).  In addition to the huge difference in resolution, those displays aren't even the same aspect ratio.  The former is 16:9, while the latter is 16:10, which means you'll either end up with black bars somewhere or a stretched image.  But even if you use Extend mode so that each display can run at its own native resolution rather than duplicating, running a 4K laptop display and a 1920x1200 desktop display simultaneously can still result in subpar image quality on whichever display is not primary.  Read this post that I wrote in another thread for an in-depth explanation of why (skip the first paragraph).

@Deb2020  I figured I'd expand a little bit on my previous reply above and offer a suggestion for the optimum setup given your hardware and preference for running Duplicate mode.  As I hinted at above, a 4K laptop display and a 1920x1200 external display is a bad combination, and it's even worse if you want to run Duplicate given the difference in both resolution and aspect ratio.  But if you want to make the best of it, here's what you'd do:

• Manually set your laptop's built-in display to 1920x1080 resolution rather than 3840x2160.  Then set the scaling to 100% rather than the 200% or so that you were using before when running 3840x2160.  You'll almost certainly notice the drop in sharpness from running only 1/4 of your original resolution, but if you're duplicating to an external display that doesn't have 4K resolution, then you have to work with the lowest common denominator here.  However, setting the scaling to 100% while running that resolution should keep things the correct size on the laptop display, AND will avoid the scaling issues I described in that post I linked, since those come into play only when running displays with different scale factors.
• Finally, run the U2412M at 1920x1080 as well, matching the laptop's built-in display -- not the U2412M's native resolution of 1920x1200.  Since the U2412M's native resolution is 1920x1200, with this setup you'll either see black bars along the top and bottom edge (since you're not using the display's entire vertical resolution) or else you'll see an image that's been stretched vertically to fill the U2412M's panel area.  You'll have to decide which is preferable to you, and I believe the U2412M has scaling settings within its on-screen controls to allow you to make that choice.

Finally, note that when changing the scale factor of the primary display, Windows will apply the change immediately by applying post-render GPU scaling, but that won't be as good as Windows changing its internal rendering scale factor.  For that to happen, you'd have to completely log off and back in to your Windows session, so do that after dropping your laptop's resolution from 3840x2160 to 1920x1080 if you want to see optimum results.

The catch here of course is that the optimum way to duplicate to your U2412M involves running your laptop's built-in display at a much lower resolution than native.  That in turn means you'll have to decide what you want to do whenever you're NOT connected to that display.  You can either a) deal with the inconvenience of switching your laptop display's resolution and scale factor back and forth as you switch between having the U2412M connected or not (and logging off and back onto Windows for optimum presentation after making that change), or else b) keep your laptop display set to 1920x1080 full-time to avoid that hassle, at the cost of not using the extra resolution of your laptop's display.

@Deb2020  A 15" 4K display is a little bit better, but it doesn't really move the needle all that much.  The fundamental problem is unchanged.  I didn't explain it quite as well as I should have above, but it boils down to this: If you mirror a display, then you have to use the same resolution and same scaling settings on both displays.  If you have two displays that are running the same resolution but have significantly different physical sizes, as is the case with a laptop display and any desktop display, then you'll have two very different pixel densities in play.  That in turn means you'd want to use very different scaling settings on those two displays -- but you can't do that when you're mirroring.  You have to choose one, and there won't be one that works well on both displays.  You can optimize for one, or the other, or accept a compromise that will be pretty bad for both.  If on the other hand you want to maintain consistent pixel density between displays so that you can run the same scale factor across all of your displays, then you'd need to increase display resolution as you increase display size.  But if you're starting from 15" 4K, scaling up to even 24" size means a significant increase in resolution in order to maintain that same density, and 4K is already the max that your system will run, so you're stuck.  And even if that weren't an issue, this scenario assumes using a consistent scale factor without mirroring, because here you're not using the same resolution.

If you want a laptop that's suited to mirroring, you generally want a 1080p built-in display.  A 13" 1080p display is often run at 125-150%, and a 14-15" 1080p display is often run at 100-125%.  Those scale factors work well on 24-27" 1080p displays.  Running 150% on a 27" 1080p display might not be ideal, but it wouldn't look ridiculous.  (14-15" 1080p displays and 24" 1080p displays are both typically comfortable to use at 100% because again, laptop displays are typically viewed from a shorter distance.)  But given that you've got a 15" 4K display that you're running at 250%, there just isn't an external display that would work well at that scale factor.  The closest you could probably come would be a 24" 4K display, which would normally be used at 200%, but 250% might actually look ok.

HOWEVER, now you're saying you don't use the built-in display at all while connected to the external display?  In that case why did you say you wanted to use mirroring earlier?  Mirroring by definition means using two displays that are displaying the same image.  If you don't intend to use the built-in display while using the external display, then yes Second Screen Only is the way to go, and then none of this matters anymore because when using only your external display you can use a scale factor that's comfortable for you there (probably 100-125%) and then go back to 250% when using your built-in display.  At that point, the only inconvenience will be that when switching between those two displays and therefore switching scale factors, you'll want to log off and back onto Windows so that Windows changes its internal rendering scale factor to match the new one you're running, rather than continuing to use the original scale factor internally and using GPU post-render upsizing/downsizing to make it fit the new scale factor.  The latter makes things the right size for your new scale factor, but they won't look as good as they will if you log off and back on so Windows starts rendering for that scale factor in the first place.