1. You definitely need to upgrade, C3700 is still a 802.11n one which is too old.
2. Prefer to separate them.
3. If you hire someone to run cable, run some ethernet cables to desired places for various WiFi AP connections.
4. When you have the ethernet connections from #3, you don’t need mesh any more, hard wiring WiFi APs together is the way to go.
5. If you go for #3, why not just let them fix (or re-do)?

It really depends on use case, if I don’t need it, then I wouldn’t care. Previously I bought the no USB Netgear WAX206 and flashed to OpenWrt, since it’s marketed as small business AP so the signal range was way better then most devices I can find in similar price range. USB? I don’t need it on a router so I am OK.

The ToH sometimes might not be very updated, but you can check the firmware selector:

https://firmware-selector.openwrt.org/?version=23.05.2&target=mediatek%2Ffilogic&id=cudy_wr3000-v1

For more details I recommend you to discuss in OpenWrt reddit sub or their forum.

Cudy X6 or WR3000

Cudy X6 or WR3000, they are just a bit over $40 and should be good for latest 23.05.2

Just a home router in AP mode would work for you.