The economics of a Postgres free tier (via) Xata offer a hosted PostgreSQL service with a generous free tier (15GB of volume). I'm very suspicious of free tiers that don't include a detailed breakdown of the unit economics... and in this post they've described exactly that, in great detail.
The trick is that they run their free tier on shared clusters - with each $630/month cluster supporting 2,000 free instances for $0.315 per instance per month. Then inactive databases get downgraded to even cheaper auto-scaling clusters that can host 20,000 databases for $180/month (less than 1c each).
They also cover the volume cost of $0.10/GB/month - so up to $1.50/month per free instance, but most instances only use a small portion of that space.
It's reassuring to see this spelled out in so much detail.