This is one of those things that are so easy to over think :) the Play/Pause button (I THINK - NOW I AM NOT SURE) by convention shows the Desired state because you press Play to Start but in other cases I would say it's usually the otherway around. Ie Check Box has a tick/cross etc when it's True/On/Yes/etc. I think the Play/Pause is a convention that is the exception
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My rule was generally Verbs show what the button will do, an adjective/description of a state will show what is currently happening.
I thought about it for a bit but Play/Pause is weird. In modern UIs the buttons follow this (⏸ appears when playing and ▶️ appears when paused) but thinking of video and audio hardware like VCRs and DVD players, you'd commonly see "▶️PLAY" and "⏸PAUSE" on the screen after pressing the button which is just feedback to show that the button press worked, but makes it more convoluted in my mind.
I agree with the action as a label.
Since it's a button it should show the state it will change to on clicking it.