I want to use a Galarian Zapdos on a new Scarlet/Violet team I'm constructing, and one of the moves I want for it is Throat Chop. Unfortunately, despite learning it in Gen 8, Gen 9 Galarian Zapdos has no TM compatibility with Throat Chop. So my question is can I transfer my Gen 8 Galarian Zapdos which already knows Throat Chop into my Gen 9 game and still have it know Throat Chop? Or is that not allowed?
Home stores movesets in a per-game mode since the BDSP/Legends update. Pokemon stored in HOME will have up to 4 movesets: Bank/Let's Go/SwSh, BDSP, Legends and SV.
Since the SV update, moves known in one of those can be reminder when transfering to a different one, IF the move is in the learnable moves list for that game.
So, you can't get Heat Wave in Zapdos in BDSP, as there is no way to teach Zapdos that move in those games, but, if your Bank Zapdos had Heat Wave, if you send it to SV you can teach it said move from Home, without using a TM.
source So roost Gliscor is illegal in SV because roost doesn't have a TM in SV.
Also Galarian Zapdos can learn throat chop directly from the TM, so you should be fine. source