KiCad V6 has many, many improvements (about 3 years of development), and upgrading at some time is indeed highly recommended.
I do fully understand that you want to keep with KiCad V5 for a while, especially if it determines whether you can pay for your house and sandwitches next week.
KiCad V5 and KiCad V6 are not really compatible with each other. I was working with V5.1.x and KiCad-nightly V5.99 for some time (and as a hobby), but only one stable version works “normally” at this moment.
If you want both V5 and V6, then you have to resort to stuff like virtual machines, flatpak, dual-boot or even two PC’s (PC’s are cheap these days, a 2nd hand USD 150 PC is perfectly capable of handling moderate complexity KiCad projects).
KiCad V6 can work with older libraries for schematic symbols. There is a Eeschema / Preferences / Manage Symbol Libraries / Migrate Libraries, but I think it’s optional.
Schematic file format has changed extensively for KiCad V6, and there is no back-conversion possible that I know off.
KiCad’s files are human readable text files, and the most reliable way to inspect your own libraries are with a text editor.
KiCad V5 always relies on external libraries for schematic symbols. If it can’t find the right library it shows the dreaded [??] symbols in the schematic. This also means that if the libraries themselves would be damaged, you will not be able to see any of the schematic symbols (in KiCad V5) in any schematic that uses that library.
A quick check if your KiCad V6 installation does something with the V5 libraries can be done by comparing file sizes and file change dates. A much more reliable / robust way is to use a source-code comparison program, for example (FOSS) http://meldmerge.org/
A sand which is completely different from a sandwich. If you try to eat the former, she’ll get very angry and you don’t want an angry which in your neighborhood.