You’re wildly overthinking this
... because you’re trying to chintz out on service panels (and only have one service panel). Our #1 advice around here is “don’t chintz out on service panels” :) Experience has shown people always regret short-changing themselves on panel spaces. (Other than that, we love to help you save money!)
You need 2 panels.
First, is the “utility-side” AC panel which gets mains power directly onto it “like normal”. All the circuits you don’t want on battery power go on this panel.
What also goes in this panel is a battery charger whose job is to keep your battery bank at full charge and also power any loads on the battery-side system, so just like your car’s alternator, it runs lights, radio and also recharges the battery. This battery charger is always-on (except when utility power is down, obviously).
Second is the inverter-side AC panel which gets its power from the inverter. All the circuits you want to work on battery go in this panel. And yeah, that can be “pretty much all your circuits” and that is fine, if the provisioning calcs support that.
You might also find it worthwhile to have a third DC panel for loads which are able to run on battery voltage directly. Common AC panels from Home Depot have excellent quality, fitment and price; but only the Square D “QO” type can support DC. Dirt-common QO breakers can handle up to 48 VDC; for up to 120VDC talk to a competent Square D/Schneider dealer, the kind that’s open 5 days a week and is open 7-5.
Simply run off the inverter 24x7
You can use a transfer switch if you really want to, but it sounds like you’re using off-grid/home-power gear here. That stuff is designed to run 24x7. So you might as well.
At that point, you don’t need a transfer switch, since your inverter-side AC panel is simply always on inverter.
However this arrangement requires all power used in the home to come through the battery charger mentioned up top. It’ll need to be sized for that, but that’s not as bad as it sounds: The inverter can borrow from the battery itself when load exceeds charger capacity. The charger will simply “catch up” when the peak load abates. The charger only needs to keep up with average loads. So if your average load is 500W and your peak load is 6000W, a 1500W charger will be plenty.
The huge downside to a transfer switch is a) you get smacked with utility-side power spikes when on utility; and b) no power whatsoever for a significant amount of time while the transfer switch is being thrown and the inverter is spinning up. By “significant” I mean your desktop PC will crash, you’ll need to reset the clock on your microwave, etc. I suppose you could put the PC on a UPS, but now you have a PC tier UPS being fed by a whole house UPS... and that’s just wasteful.
The other thing about “always-through-inverter” is it will absolutely suppress any power spikes from outside. The battery charger will take the hit, but the DC-AC conversion makes it impossible for them to reach your inverter-side panel.
For your internal power spikes (refrigerator starting etc.), you’re on your own. For that, fit a whole-house surge suppressor.