I thought there's a NOSTR based calendar tool, too.... ahah, there is this:
https://nostrcal.com
In addition to that, I use Calendar tools from Fastmail, which I pay $90/year for... it comes with email & masked email & a lot of other things.
I don't know what sort of scheduling service could integrate with iCal, but that's a hosted implementation that's not gmail... it's Australian tho, so you're still owned by the 5-eyes & it's not open source... but it's protocol based.