If you want to access a bloom filter, cuckoo filter, list, set, bitmap, etc... from multiple instances of the same service, Redis (slash valkey, memorydb, etc...) is really your only option
It also has arrays, sets, and bitstrings, though for the latter you can just as easily (and with less space consumed) map it in your app, and store an integer.
this seems like a classic case of impedance mismatch, trying to implement a Redis-ism using an RDBMS.
for a shared list in a relational database, you could implement it like you've said, using an array type or a jsonb column or whatever, and simulate how it works in Redis.
but to implement a "shared list" in a way that meshes well with the relational model...you could just have a table, and insert a row into the table. there's no need for a read-modify-write cycle like you've described.
or, if you really need it to be a column in an existing table for whatever reason, it's still possible to push the modification to the database without the heavy overhead. for example [0]:
> The concatenation operator allows a single element to be pushed onto the beginning or end of a one-dimensional array. It also accepts two N-dimensional arrays, or an N-dimensional and an N+1-dimensional array.
0: https://www.postgresql.org/docs/current/arrays.html#ARRAYS-M...
You’re right that managing lists in RDMSes is easy-ish, if you don’t have too many of them, and they’re not too large. But, like I mentioned in my original comment, redis really shines as a complex data structure server. I wouldn’t want to implement my own cuckoo filter in Postgres!