How do I upgrade to HDMI 2.0 from HDMI 1.4b on Dell Vostro B560 motherboard ?

Your Vostro model may be 3681. Chipset is B460. Its video port is fixed with hdmi1.4b.  This would not change if you upgrade cpu.  I suspect it is limited by chipset.  ASUS B460 plus board spec also has hdmi1.4b.  
upgrading motherboard or cpu for 10th gen is more costly than getting a discrete video card that supports 4k 60.  Also updating Dell modern proprietary  motherboard is nearly impossible given its nonstandard form factor and connectors.

one user states that “The only "true" HDMI2.0 - 4k/60hz card within the "GT" series of media chips is the GT-1030”.

if your monitor has DP port, consider a discrete video card that has DP output.  The DisplayPort output port must be DP 1.4 compliant to get 4K @ 60Hz with HDR or DP1. 2 for 4K@60Hz without HDR.

Vostro 5690 spec mentions only hdmi1.4b video port.  I am not sure if that can be changed to hdmi2.0 if you upgrade from 10th gen i3 to 11th gen cpu i5/i7 in this model.

It is possible that the spec covers overall hdmi capability without getting into details of various cpu.  use the spec below for reference.  You may need to call Dell tech support to ask for detailed technical validation of i5/i7 in this model.

Asus B560 motherboard states

1 x DisplayPort 1.4
1 x HDMI 1.4

*Graphics specifications may vary between CPU types.

** For Intel® 11th & 10th processors, support DisplayPort 1.4 with max. resolution of 4096 x 2304 @60hz. 

***Only Intel® 11th processors support HDMI™ 2.0 with max. resolution of 4K@60Hz, others will only support HDMI™ 1.4 with max. resolution of 4K@30Hz.

Thank you redxps630 !

My Vostro is 3690 with B560 chipset.  Will it do ?

It has no PCIe 16x for a discrete graphics card, just a PCIe 1x left(or 2x ? who knows ?) nearby power adapter, short, for audio card or the like.

BTW, another question, if you're free.

My Vostro 3690 with i3 10105 in has a SK hynix 256GB SSD on claimed "M.2 PCIe SSD-0"(2230/2280), no version provided. And manual does not say it's PCIe 2.0 or 3.0 either.  Do you know ? Thank you in advance.

Thank you so much redxps630 !

Dell staff just replied me,  no upgrade from HDMI 1.4 to 2.0 is available in my case.

Even UHD 630 graphics in i3 10105 or 10100 supports 4k at 60hz, but it has to be a DP. But my Vostro 3690 has no DP nor PCIe 16x Slot for a discrete graphics card which is the issue.

If I had known this when buying I would have bought 3681.

not sure if Dell B560 board is designed to have less HDMI bandwidth than other B560.

ASUS board mentions only HDMI1.4 in spec but does add small print of "only 11th gen cpu supports hdmi 2.0"

MSI board spec mentions "∙ 1x HDMI 2.0b with HDR port, supports a maximum
resolution of 4K 60Hz*/**

* Available only on processors featuring integrated graphics.
** Graphics specifications may vary depending on the CPU installed"

so there is a chance that Dell spec is generic (covers basics only) and not detailed enough, and Dell support does not know the nuance.

if you have no other option, try one of the two following cpu.  worst case you still get a newer higher core cpu than your current i3.

11th Generation Intel Core i7-11700

Thank you so much redxps630 !

Yes, I though then. That's why I answer the first question. But there's a probability that Dell B560 board is different from Asus B560 and MSI B560.  As follow is table of HDMI version(i5, i7 covered) on my Vostro 3690 manual. They're all HDMI1.4, whether it's i3, i5, i7 or not. Is it the way Dell goes ?