Do dedicated AP devices (I am thinking of commercial wifi networks) work as mesh? One SSID to rule them all, and just connecting to the one with the best signal.
No
(and sorry for slow replies, i went on holiday)
Using AP's with the same password and SSID will possibly bounce you between them but since you're on seperate networks any active sessions will crash out when that happens - changing from one router to another will be a different IP address and your traffic will get lost. You'd get booted from games, voice calls, etc.
Using just an AP or repeater seperates the networks and is designed to only really work for basic internet access, not incoming traffic - you would need port forwards for any incoming traffic to reach you, and since ports can only reach one device it's a major obstacle for any peer to peer technology like player hosted gaming - if you port forward from router 1 to router 2 and router 2 to Gaming PC1, no other device on the network will ever receive inbound traffic from that port - UPNP for example can't dynamically move it around as needed.
Mesh devices usually have to be the same brand and even then support is limited to specific matching products - The one downside is you usually have to buy what you need in one hit (But 3 pack budget mesh setups are cheap and good enough for anyone)
By connecting you to the closest one and being aware of each other, they can have each device use as little transmit power as possible which reduces interference, as well as keeping every device on the same subnet (IP address range) - this lets things like local file transfers, printers, chromecast, wifi camers etc etc to see each other - and changing between them is seamless with no packet loss or connection drops
If you use a wireless AP they're all independent and unless you disable the DHCP server it'll be a seperate network so while devices on each router both have internet access, they can't access each other (see examples above)
Usually what you'd do is set it up like so:
(For this example, router 1 is 192.168.1.1 and router 2 192.168.2.1)
With the normal use, you'd have those two different ranges - anything on 2.x can't communicate with 1x2 devices, but both ranges have internet.
Router 2 would have its WAN port as 192.168.1.x and LAN as 192.168.2.1 while handing out 2.x
To set it up without breaking the network:
1. Wifi name and password you want (Different SSID and channel to the first routers wifi)
2. Set a static LAN IP address for it, within the range your other router uses (192.168.1.100)
3. Disable the DHCP server (You will lose access to it's login page at this point)
4. Connect Router 2's LAN 1 to router 1's network - DO NOT USE THE WAN PORT
This sets it up as a basic network 'switch' with the wifi working, letting the original router do all the thinking, so QoS and uPNP can work correctly.
You can repeat this for every extra AP you add in, but keep in mind there's technically only three 2.4GHz channels - 1 7 and 11.
The others share with those, and 40MHz devices need to use 6 channels (1-6 or 7-11)
Since bluetooth and most cordless devices also use the 2.4GHz band, you'll find that multiple 2.4GHz AP's will absolutely screw with you - low power devices like bluetooth become line of sight, game controllers get glitchy and so on.
Personally, if I can't use mesh I'd use one central 2.4GHz location set to 20Mhz for low bandwidth devices like smart lights and legacy devices, with just 5GHz at every other AP's location (since there are more channel options, and since 5GHz has far shorter range)
(I added a lot to this after writing initially, sorry if it's not in the best logical order)
