How safe is SHA-256 now? Or Is SHA-512 needed in the near future?

Safe enough, but why not use a modern hash function instead?

What are some of the modern hashing alternative for uniqueness? Mainly for speed, bit distribution, and collision risk while having small hash size. Not for cryptographic purpose.

dependenttypes

Depends on what you want to do. For hash tables and macs there is siphash. There is also Chaskey (although this is optimised for embedded systems I think).

eadan

Also in the super fast, but not designed to be cryptographically secure category:

xxhash (https://github.com/Cyan4973/xxHash) with 32/64 bit output. The latest version, xxh3, supports up to 128 bit output.

meow hash (https://github.com/cmuratori/meow_hash)

The recently released Blake3 which is designed to be cryptographically secure is very fast also (https://github.com/BLAKE3-team/BLAKE3)