Authentication without decrypting the password?
This can be done with a cryptographic protocol called Password-Authenticated Key Exchange (PAKE). It comes in a few flavors:


Plain PAKE is a good fit for peer-to-peer connections. Both participants know the password in the clear, and use it as input to the PAKE protocol. If they both agree on the password, then they establish a shared secret key, safe from eavesdroppers. If the passwords disagree, they fail to establish a key.
Asymmetric PAKE (aPAKE) is a good fit for client-server connections. The client knows the password in the clear and the server holds only a "hash" of the password. (In practice, it's not exactly a hash but something more involved. The point is that the server doesn't know the password in the clear.) The two participants will establish a shared secret key only if the connecting client uses the correct password.


A good, accessible introduction to the state of the art can be found in this talk by Hugo Krawczyk earlier this month at the Real World Crypto symposium. Among other things that you can do with PAKE, he explicitly talks about aPAKE as a replacement for password-over-TLS (the typical approach for authentication that you described).