I completely agree with climbing gyms!
I'm lucky enough that I live in a city that has a newbie-friendly group that climbs every week and goes for dinner and board games afterwards.
I consider myself an introvert, but after going for a while, I got to figure out who are regulars, and they recognise me as a new regular too, at which point they're more open to socialising more, even outside the weekly meetups.
Even when I'm bouldering alone, I've had random people cheer for me when I'm about to send, or show me the beta for a route I'm struggling with, or ask for help with a problem. It just provides a very natural conversation starter, at which point you can pivot to other topics, provided they seem open to talking more.