Tristin
I have not used an a7riii but the EVF is, according to long term Sony users, supposedly better than the a7iii.
I have very occasionally noticed a 'shimmering' of the EVF image on my a7iii. Z6 Has better EVF.
I have been using EVF since original EM5.
For action I still prefer OVF.
One thing to be aware of is listening to those who rave about "What you see is what you get". That really depends on what settings you are using. There are many inter-dependencies of settings and some are not consistent to what you might be shooting.
I rarely use all the functions of any camera. I do not shoot vids but I am very interested in AF, viewfinder lags, auto ISO, auto WB, metering and Buffers. Those may not be that important for your shooting.
The a7riii has dropped in price big time.
Both a7riii and a7iii are much more responsive , faster and good battery life. Lags are not as bad. For my shooting the a9 is best Sony (action) but I bought Z6 for my long Nikon lenses. You will have a learning curve going from OVF to EVF And DSLR to MILC. Sony menus are not great.
This is from my phone so hope it makes sense