The tl;dr for this is: yes, you can just upgrade Prysm by stopping your services, copying the new binaries and then restarting your services. I had to do this recently as the Altair fork required all clients to be running V2. Unfortunately, the official docs on upgrading only provide instructions based on three different ways of installing: Prysm.sh, Docker and Bazel. I did not set up Prysm via any of these routes.
Recently, I set up an Eth2 node with a friend. Eth2 refers to a series of upgrades planned to make Ethereum more scalable, secure and sustainable. The main part of this upgrade is a move to the beacon chain which operates on Proof-of-Stake (PoS), as opposed to the Proof-of-Work (PoW) consensus used by Bitcoin, amongst others. As you have likely already heard, Bitcoin’s Proof-of-Work consensus currently consumes more energy than all of Argentina, which is one of the many reasons for newer cryptocurrencies considering the less energy-intensive Proof-of-Stake mechanism.