I'm currently renting a small VPS for my self-hosted services, and I have some spare capacity. So I was wondering, are there any downsides that I might be overlooking?
My self-hosted services are on a URL with my real name. Could there be any privacy or legal implications for me? (I don't live under an authoritarian regime)
Yes. People use these services for nefarious reasons. If that activity is captured and able to be processed into a usable format, you will be in trouble. Snowflake should be used only for your own personal purposes.
I skimmed over the page you linked and it sounds like an 'exit node', or more precisely, just a proxy. So all the traffic looks like it's coming from you.
From OP's link under the "operate a Snowflake proxy" section
You can join thousands of volunteers from around the world who have a Snowflake proxy installed and running. There is no need to worry about which websites people are accessing through your Snowflake proxy. Their visible browsing IP address will match their Tor exit node, not yours.