I'm trying to wrap my head around this.

Ignoring transaction fees, if I have a public key with 5000 sats, but only intend to send 2000 sats, I would send the transaction to address btc.....123 the intended recipient, and the system creates btc...456 which is my own wallet. The first public key gets the 2000 sats and the remaining 3000 sats get put back in my wallet at the newly created address, which is the refund.

So one UTXO is only good for spending 2000 sats and the other UTXO is only good for spending 3000 sats. Those UTXOs at the recipient or refund addresses can then be split up or combined in their respective wallets with others for the next transaction. This is how I understand it.

It makes sense that you want to completely destroy the previous container(s) of sats and forge new ones in exact amounts.

I read something similar with Dash staking in which you need to send your wallet balance to your own address so that all the individual pieces received at different addresses from the same wallet are combined into one so that the validator can confirm you have the required amount of Dash.