Just thought I'd reply with my thoughts.
I've been using Canon DSLRs since the 40D, currently still have a 5D mk1, and mostly use a 5D mk3. (Previously had Minolta film SLRs and their first digital body - the Dynax 5D).
I really like full frame - there was a noticeable change in the overall quality of the image when I moved from the 40D to the 5D. I know this is really old kit, but personally I wouldn't consider moving to a smaller sensor (whether DSLR or mirrorless).
As the 5Dmk3 is also now quite old in terms of tech, I've been considering a change of body, mainly for improvements to low light performance and quality, but also keen on potential AF improvements (especially stuff like eye and animal tracking).
It looks like the future is definitely mirrorless, with Canon stating that they will be concentrating on this route and have apparently abandoned development work on the 5Dmk5. They also stated that they will not be releasing new EF lenses and have recently discontinued 24 of their existing lineup. (Some info towards the bottom of
this article)
In terms of mirrorless, Canon have been lagging behind the other manufacturers, especially Sony, but with the release of the R6 and R5, and now with the announcement of the R3 (and potential future R1), it looks like they have definitely caught up. They also appear to have caught up in terms of low light performance too.
GIven that you already have the Canon 24-70 f4 and 70-200 f2.8, and the fact that these (and other EF) lenses apparently work very well on the R series bodies with the Canon adapter, in your position, I'd definitely be leaning towards the R6 rather than the 5Dmk4. By the way, it looks like the Sigma 10-20 f3.5 is a "DC" (EF-S) rather than "DG" (EF) Sigma lens, so although not fully compatible with the EOS-R6, it is still apparently usable on that body, but the R6 would switch to "crop mode" producing an image equavalent to an APS-C sized sensor rather than full frame (see responses on
this forum thread)
Also staying with Canon, as opposed to switching to another manufacturer means that you are already familiar with the feel and operation of the menus/user interface (something which should not necessarily be dismissed as a small thing).
As has been suggested, perhaps look into hiring an R6 for a weekend to see how you get on with it?
For me, I think I've already decided that I'll be looking to move to a Canon R5 and continue to use my existing lenses with the adapter. Any new lenses I'd possibly buy in the new R fitting (although this has the disadvantage of not being able to use them on the 5D3), but am expecting many years further use of my existing lenses (which is good, as it would be pretty expensive to replace them all). By the way, it looks like Canon really have done a great job of ensuring backward compatibility for EF (and EF-S) lenses enabling a very smooth path to adopting their mirrorless bodies.
In any case, good luck with whatever you decide.