Just for reference, the Apple AirTag has a built-in Bluetooth beacon, that broadcasts its location information every 3-5 mins. It is a very low power beacon with a range of around 30'.
If your Lexus key fob also uses Bluetooth, my guess is that it only sends a signal when pressed. If its battery is draining rapidly, would indicate (to me) that this fob is broadcasting constantly. How the AirTag can interfere with that fob, specifically on draining it battery is unknown to me.
FWIW, I don't have a 2023 Lexus, or any model Lexus, but have a number of vehicles that employ remote key fobs ... and none of them have had any issues with the AirTags connected to the same keychain as the fob with draining their batteries. Could it be that your particular key fob is defective?