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.