Proof of stake computational work?

Hey so I have a question regarding the computational work being doing in ethereums pos environment (but really it's a broader question to a proof of stake environment as a whole).

My understanding is between pow and pos, you're no longer relying on the computational work to race to generate new hashed blocks, you're shifting over to holders staking an amount of eth to generate new blocks. My question lies in where is the computational work being done? A computer or rack of ASICs still have to be present to generate the hashing power to log the transactions, and broadcast it out to the ledger, so who is doing that and/or how is that being done?

I understand algorithimically it's deciding that x person has y amount of staking power because they staked y eth, but where then is the offloaded computational work being done? Because it seems like most staking is happening through your wallet, ie you stake through Coinbase, or Kraken etc does that mean Coinbase is doing the computational work?

Somehow in some shape or form hashing has to be done to generate and continue building upon the ledger, which means a farm or series of miners have to be employed, no? Or am I completely off base with my understanding of pos?

I googled and searched here as much as I could. So any info would be appreciated!