why is it considered a standardness rule instead of a consensus rule?
Because you can change it and Core doesn't reject blocks with large OP_RETURN
Who or what determines that?
Anyone that runs a node. If you change a consensus rule you will fork off (reject blocks or others will reject yours) but if you change a standardness/policy rule, no such thing happens.
what's stopping miners from giving themselves a higher block reward
That is a consensus rule. Your node will reject a block where a miner issues themselves more subsidy due to those rules.
OP_RETURN