Are you looking to self-host, or are you okay with using managed services? If your dataset has like 10's of thousands of rows and handles many queries, then I think you might find Planet Scale to be quite expensive considering the fact that you pay for every single row that queries search through. Personally, I think Oracle Cloud free tier is ideal since their compute and networking are top-notch for the price. They also give you 10 TB of free transfer per month and have bandwidth alliances with multiple CDNs.
If you don't have to use PostgreSQL, or it's not required for every query, you can use Aerospike as a secondary store for insanely fast lookups. In benchmarks, Aerospike on disk outperforms Redis and all other caching servers by a large margin, and the free version come with very generous use abilities.
ClickHouse might also be a faster alternative to PostgreSQL, but required a lot more to setup and isn't as straightforward. But it should allow you to use less compute while performing better than PostgreSQL.
I also think that Planet Scale and SingleStore both have backward compatibility issues, so you could really screw yourself over by using them, then deciding to move to a different database and/or provider.
Anyways, if you want managed, here are some database providers that I know of that have serverless pay-go options:
https://www.cockroachlabs.com/pricing/
https://planetscale.com/pricing
https://www.pingcap.com/tidb-serverless-pricing-details/
https://neon.tech/pricing
I mean there are more, but I can only personally vouch for Planet Scale.