Supabase defo has a much higher mindshare.
This is like if Google Spanner were open sourced tomorrow morning: realistically how many people are going to learn how to deploy a thing that was built by Google for Google to serve an ultra-specific persona?
Maybe you might get some Amazon-sized whale peeking at it for bits to improve their own product, but the entire value prop is that it's a managed service: you're probably going to continue paying for it to be managed for you.
I always loved Vercel for their easy hosting of Next.js with included CI/CD, but I recently switched to self-hosting - their pricing switched from a flat, worry-free $20/month to an unpredictable whatever-it-may-cost plus it sent me 10+ emails every single month about hitting some quotas that they introduced and I couldn't find a good way to stop that.
They also offer so much more than just postgres. Though I use them only for postgres myself.
It's easier to just become familiar with a DB UI tool like Beekeeper or DataGrip and spin up your own things. I'm also not a huge fan of being "locked-in" to so many things (including their auth). I think most projects would be better off keeping these parts separated, even if they are using third-party services to handle them, as it would be way less overhead to migrate out.