Generator Transfer Switch for 2 Panels

I’d like to install a Transfer Switch (10 circuits) from the Generator to the two panels I have. Each panel is rated at 200 amps. If I turn off the main breaker in one of them, the other panel still works and vice versa. But I did find that the ground and neutral in both panels are all connected to each other.

So if I mount a transfer switch near them, would there be any issue if 6 circuits go to one panel and 4 circuits go to the second panel. Since the transfer switch only has one ground wire I believe and because the neutral and ground are connected in both panels, it wouldn’t matter whichever panel I connect it to.

Any thoughts if this will be an issue?

Update

I can certainly try to go over the breakers that are critical and have an electrician move them over to one panel and then use a generator interlock switch on the top 2 right breakers, so either those 2 breakers can be on (powered by the generator) or the main breaker can be turned on. There are no spots for new breakers left, but the panel on left is smaller, so I can look into getting a bigger panel that’ll allow more circuits

These transfer switches are definitely very expensive for only few circuits. But from theoretical standpoint, can you tell me why the transfer switch’s 10 circuits can’t be connected to two different panels, when the neutral/ground in both panels are connected to each other. (So the one neutral wire from the transfer switch can be connected to any panel)