Novalissoide Thanks for confirming that it works for you.
I uninstalled both Maps and Android Auto. So I only have Play Services and Store installed. And it hasn't changed the behaviour.
What did work was deleting storage and cache from Vanadium. Followed by a force stop. When it reopened Vanadium was at defaults (it asked for notification permissions). And now I'm not getting the Play Services is not enabled message, even though Play Services is installed and disabled.
If I had to guess, I must have browsed something (perhaps testing location with google and apple maps) with Vanadium when Play Services was enabled and something got cached or stored that was persistently looking for something the compatibility layer doesn't provide. Well that's a guess.
Those other apps that were requesting Play Services are probably PWA apps using Vanadium's Webview. So perhaps that's why those apps were doing so because they have stopped being noisy too.
I'm not sure if there is a bug here or not. I have no idea how to reproduce it. If it was some cached Play Services request that could be a bug because I had all the tabs closed in Vanadium.