Hmm...So I have Telegram installed via F-Droid (so presumably without Google Play Services). I do NOT have the "People Nearby" feature. I am curious if that means my location is not published?

The F-Droid version unfortunately seems helplessly outdated.

I wouldn't call it helplessly outdated, at most it's a version behind. But there's a number of reasons for this. For starters Telegram themselves lag behind in releasing the source code for the app[1]. Then the volunteers who make the FOSS version[2] have to update their fork and make sure it works. Then finally it's submitted to F-Droid, where it's compiled by their build servers (of which the build process occasionally breaks and needs to be fixed).

I think the assurances that this offers (entirely FOSS, reproducible builds, better privacy and security[3]) outweighs being sometimes days or weeks behind the releases they upload to the Google Play Store.

[1] https://github.com/DrKLO/Telegram [2] https://github.com/Telegram-FOSS-Team/Telegram-FOSS [3] https://github.com/Telegram-FOSS-Team/Telegram-FOSS#changes