Proof of Stake at the end of the day is just saying “instead of joining a mining pool and paying my electricity and hardware to do a lot of wasteful work, I’ll instead pick another entity to do the mining for me and give me a share of the profits”. Proof of Stake is still Proof of Work,

It’s literally not this. Proof-of-stake is basically saying “I’m allowed to author the next block because some math formula says a coin I hold is eligible to do this, and here’s a signature proving I own the coin”. It’s not proof-of-work, it’s proof-of-ownership.