To be honest, I think none of them have seen the entirety of Star Trek.. That would be a ridiculous burden.
It often feels like they have a reference catalogue lying around - like a cliff's note of previous Trek lore ("Section 31 = shady Starfleet spies"; "Khan = Kirk's genetically engineered arch enemy"; "Kirk = womanising hero guy";...). They are constantly referencing stuff. But it rarely feels they actually watched the stuff they reference. A bit like the MARVEL catalogue where the MCU writers come to to pick up names, ideas & scenes, without needing to read decades of rubbish comics.
Shows the good side of the TNG era approach, where previous Trek was mostly ignored & referenced sparingly, as new writers could come in with their own ideas easily. Now every new thing somehow needs a connection to an old thing, and the connection itself often feels kind of wrong. Too much focus on IP & lore, too little on story.