The bios of my 3471 can't detect my Kingston A400 SSD

I hope you didn't corrupt Windows on the HDD by changing BIOS to AHCI without preparing Windows for that change, first. So put BIOS back to RAID and see if Windows still boots before you go any further...

There are 2 M.2 slots on the motherboard, one for an SSD and one for a WiFi card. Did you put the SSD in the right slot? See page 14.

What version of BIOS is running now? The latest is 1.4.0. Don't update BIOS until you're sure the PC boots from the HDD again, and maybe remove the SSD before updating too. Instructions to update BIOS are on the linked page. Read/follow carefully. If you decide to update BIOS, I'd follow the instructions for: Updating the BIOS from BIOS Boot Menu (independent of operating system). Keep in mind that there's always a risk a BIOS update will fail and brick the motherboard.

new blank drive wont show up in bios as a boot option before its partitioned and formatted

I did it like the guy in the video below (at 2:20, last half minute of video)

Same type of SSD only different brand

https://youtu.be/EnGQkvmuX8Y?t=140

The PC is running fine, I just finished gaming after a few hours. No issues.

My Bios version is Dell Inc 1.2.0, date 7-1-2020

I can not partition it because it's not detected at all. not in the bios and not in diskmgmt.msc

I want to copy the OS to the SSD. I saw a video of someone explaining this process but can't find the video back

You can use Macrium Reflect software (free) for this. But you should configure Windows to use AHCI first because some SSDs don't like working with RAID.

1. At the desktop, open a Command prompt window, Run as administrator
2. Copy-paste this command, which will start Windows in Safe Mode the next time you reboot:
   bcdedit /set {current} safeboot minimal and press Enter
3. Restart the computer and enter BIOS setup by tapping F2
4. Change the SATA operation mode from RAID to AHCI
5. Save the change and exit Setup and Windows will automatically boot in Safe Mode
6. Open a Command prompt window again, as in step #1
7. Copy-paste this command, which will start Windows in Normal Mode the next time you boot:
   bcdedit /deletevalue {current} safeboot and press Enter
8. Reboot and Windows will automatically start with AHCI drivers enabled

Now clone the HDD onto the SSD with Macrium Reflect. When that's done, reboot the PC and start tapping F12 to open the boot menu. Select the option to boot from the new SSD. If you just boot normally, PC will only boot from the HDD.

After it boots from the SSD, make sure everything works ok and your files are all safely stored on the new drive. Then open Windows Disk Management and initialized the HDD. (ALL FILES WILL BE DELETED!)  After initializing the HDD, reboot normally and PC should boot directly from SSD and you can now use the old HDD for storage.

Then configure Windows to move default folders onto the HDD, and configure your installed apps to store their output on the HDD too, to save space on the new SSD.

I did the first steps: cmd > safemode > reboot > F2 > AHCI > apply changes

system rebooted a few time, showed only Dell logo. Than it went  to an assistance for boot check and OS recovery. I had to do the Bitlocker thing and no SSD could be found.

I think I send this SSD back as well.

What SSD's are recommended for this pc?

Can I also do SSD via USB? I saw someone doing that in a video. I've booted a lot of pc's with a Linux OS on USB-stick so perhaps it could work with SSD with USB connection?. 

Crucial lists several SSDs they say are compatible with the Inspiron 3471.

Would this SSD from crucial work? It's not in the list but from the same brand

https://www.alternate.nl/Crucial/P1-500-GB-SSD/html/product/1491529?event=search

Short answer: No

The specs say the Inspiron 3471 has a slot for an M.2 2230/2280 SATA solid-state drive.

The one you linked is an M.2 NVME SSD.