they can if they're a mesh network... but I'm not sure that's what this is.
The bit that seems odd to me is having the router from ISP being any more than a modem, I think. I have my IPS (cable) thing being in modem-only mode so that my mesh router can handle all the rest of it. But I don't like messing with network things so yeah, got a mesh setup and don't often have to think about it.
Access points can have the same ssid, both mesh and non-mesh. That's the way our home system has been for the last 5 years or so. Mesh systems do several things which are an advantage over non-mesh systems, such as getting rid of any "stickiness" during roaming, so that your phone, for instance, doesn't hang on relentlessly as one AP gets weaker and weaker, refusing to reconnect to a nearer one. Wifi coverage can be wider and stronger as well. You can achieve the same with a properly configured non-mesh system which has a network controller included, but I haven't got the time or patience for all that malarky, and anyway, if your APs are in the right place and strong enough (and are wired APs rather than repeaters), there's precious little difference in an average house.
not a big deal but annoying are the most annoying kind! You know that every minute spent on it is basically a waste of time but also they just won't let go, nagging annoying pests.
Annoying I can live with. The most annoying kind aren't *merely* annoying, they strike terror of data loss, system reinstall, and $$$ hardware replacement. :-@:'C . Sometimes you get an upgrade out of it, but lord what pain.