Lightroom Classic's catalog and Google Drive

Will we ever see this working?

I doubt it. I am guessing, as I have no inside information, but I don't think Adobe is working on this. Please read the links provided by @GoldingD 

Adobe uses SQLITE as the database engine, your catalog is a SQLITE database. SQLITE is not a Client/Server database. It is not suitable for remote access over network shares. Adobe does not own SQLITE. Adobe is not alone in this. For the capability of remote access Adobe would need to change to a more expensive database engine.

Search the Internet on search phrases such as:

• SQLITE on network drive.
• SQLITE Lightroom
• etc

Heck that is how I found most of the above info.

for example:

Well-Known Users of SQLite: SQLITE ORG

SQLite Over a Network, Caveats and Considerations: SQLITE ORG

Quirks, Caveats, and Gotchas In SQLite: SQLITE ORG

hmm, and an old bit of info, Adobe has invested in SQLITE:

https://www.cnet.com/tech/computing/adobe-funds-sqlite-database/

I mean, 2022 lol