Will a HDMI 2.1 Cable be compatible with a 720p TV?

I already know they are backward compatible from 1080p devices to 2.1 enabled TVs

Here's the Scenario....

4k 8MP Swann CCTV DVR - HDMI out > to HDMI in - 4k HDMI splitter/Downscaler (1 output to HDMI modulator 1080P, 1 output to 720p TV - this cable I don't have yet but will be routed beneath flooring so won't be easily accessible, currently the flooring has been lifted for building work, so for this reason I want to install the HDMI cable and future proof it as much as possible providing the cable will work with my current setup)

HDMI modulator along with 2 others are all wired into the TV distribution and accessible on all TV's on Freeview HD channels (Modulator 1 - CCTV Ch97, Modulator 2 - Freesat HD Ch98, Modulator 3 - Sky Q Ch 99)

All equipment is hidden out of sight in a cupboard along with all the Cat6 network switch & patch panel setup.

Why do i want to use HDMI cable when i can view over Freeview in HD already?....
There is a 1-2 second lag between the DVR and the TV due to the nature of the Modulator...
Why is this an issue for viewing?....
This is only an issue when it comes to controlling the DVR with the mouse in the room with the 720p TV, it makes it very difficult to operate with the lag...
So as I cannot stop the lag from the Modulator, my work around is to install a HDMI cable between the downscaler and the 720p TV, which will eliminate the lag thus making my life easier.

I could just install a HDMI 2.0 and be done with it, but as mentioned above the routing for this cable will not be easily accessible, so while I have easy access I want to install a HDMI cable which will be as future proofed as practicably possible over the 12 meter run.
So if I can install a HDMI 2.1 cable and it is compatible with the 1080p to 720p setup, it will be future proofed for when I eventually need to replace the TV, which will undoubtedly be a 4K 2.1 enabled TV

I thought about HDMI over Cat6 as it is all networked, but don't wish to do this as the HDMI cable on its own will be a much neater fix.

I have searched Google for hours trying to find out the answer this question but have been unsuccessful

Is there anybody out there that can answer this over complicated question for me please?

Thanks in advance