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You could use cal.com (one of the competitors mentioned in the post). The use case you described would fit into their free tier.

The platform is made for booking but you can use it to show your availability, by allowing people to request meetings and then not accepting any of the requests.

It's also free and open source, so you can host it yourself, if you want that.

Isn't available in most meeting scheduling platform? I guess you're mentioning booking a meeting/call based on availability on the attendee.

Not exactly the same but when2meet is pretty good to let others know when you are availble