But the start playing event will still be perfect for me. I want the record to be inserted inside the jukebox without playing. More specifically, I am developing a plugin that allows to record notes on records and playing them from a jukebox. If I do Jukebox#setRecord(not null ItemStack), then it immediately automatically plays (I already use this in another feature of the plugin, which restarts the jukebox when the redstone powered it).

And in general, it is more convenient to check which record is trying to start playing than to check which block is clicked, which item is in the hand, is there already a record in the jukebox, etc. (I can't even name all the checks right away)
Yes, and playing the record from setRecord can be workarounded, but why do I need all these workarounds if I can have just one event, which is quite simple and does not overload the server: just call listeners at the point before sending the packet to the players, and then check if event was cancelled.

InteractEvent is perfectly fine for this. Just check for any Right Clicks.

Also for the Jukebox stopPlaying you can do

jukeboxState.setPlaying(null);

jukeboxState.update();