Are bech32 and base58 the only address formats?

Question

Are bech32 and base58 the only formats that a Bitcoin address can use or is there another?

Answer 1

Yes. Base58 and bech32 are the only standardized address formats.

However, there exist standard ScriptPubKeys (the "locking" Script in the output) for which no address format is defined.

Answer 2

Sort of. All legacy output types use base58check (which uses the base58 encoding and adds a checksum) in their address encoding. Native segwit v0 outputs use bech32 addresses, while native segwit output v1 (P2TR) use the bech32m address encoding which is a slightly modified version of bech32. Future output types will likely also use bech32m.