I can concur with Dave's pointing out that this is possible.
1) I run multiple versions of cf on every machine I have, able to run them at once (subject to adequate resources) or turn on/off whatever one I want. I've done it with all cf versions.
As he notes, the biggest gotcha in doing this is proper web server configuration, using cf's wsconfig tool.
Another is that you definitely to leave the old version RUNNING when you install the new, as that way the new will choose different values for the several ports cf uses.
2) As for migration compat issues, there can be many or there may be none. It's totally dependent on your app and it's sensitivity to the changes in both the version you're moving TO and any version(s) you may be skipping over. Fwiw, I did a talk recently on migrating apps to cf2021 from all recent versions. The recording and pdf are available at carehart.org/presentations.
3) Finally, as for the docs not having been updated, that's a common problem: dozens (if not hundreds) of pages that refer to cf2018 (and even sometimes cf2016 and cf11) were never updated for cf2021. Same with them showing the last update date of Apr 2021: nearly ALL pages do, and it's tragic when they give the false impression you reasonably came to.
Since you work for Adobe, eualexaffonso, it would be awesome if you might be able to nudge anyone from the inside. 🙂 I've raised the observation many times but no one's picked up the baton to make a global sweep of things.
It would take perhaps a few hours for someone to do a.global find to replace (or better remove) the version number, when the reference not truly specific to that version. (That means once CAN'T do a global find AND replace.)
Hope all our thoughts help get you/your partner going.