All of those can be serialized and stored in an RDMS. You don't need Redis for that.
They can (and that's probably the right choice for a lot of use cases, especially for small data structures and infrequently updated ones), but serializing and storing them in a database requires you to (in your application code) implement synchronization logic and pay the performance cost for said logic; for instance, if you want to `append` to a shared list, you need to deserialize the list, append to the end of it in your application code, and write it back to the DB. You'd need use some form of locking to prevent appends from overwriting each other, incurring a pretty hefty perf penalty for hot lists. Also, reading an entire list/tree/set/whatever back just to add/delete one element is very wasteful (bandwidth/[de]serialization cost-wise)
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!