I'm self hosting this, and it works pretty well. It can be integrated with Google Calendar with some effort, and it works with CalDAV (which I'm using through NextCloud).
Just be aware that, while it's marketed as open source, from my last look into the project the open part relied on non-open licensing/code. More details in my blogpost here. Might not matter to some, but might matter if being open source is an important factor.
Could you explain what makes Calendly different from the hundreds of online calendar solutions that exists and can often be self-hosted? I never used it, so it is hard to make a recommendation for an alternative.
Calendy is a bit different in that you set your free time. And users request meetings with you and get booked. Cuts down on the guessing game of are they free or not. Just send someone your link and have them pick a date/time. Done.