One question just because I'm looking for a bit of clarification why this suggestion works without requiring separate SSID's. Is it because you are using Ubiquti or Aruba? In other words other routers, for example, won't necessarily support handling the shared SSIDs between the AP's or migration of the device to the best node for connectivity? Perhaps this might be more of a question how do multiple AP's manage broadcasting the same SSID without clashing with each other?
You asked several (part) question and tried packaging it as an example. Just an FYI this is usually an indication of assumption so I will try to clarify.
First. Ubiquiti, Aruba were the preffered suggestions, because they cater to soho or prosumer. They are by themsevles (minus the rest of the stack like switches and routers) not only able to be setup by themselves but given there respective apps more simple to setup than say a router. If you are daring though you can use w/e you want as far as APs
Ubiquti
Aruba (HP)
Mist (Juniper)
Aeronet/hive (Cisco)
Ruckus
They will all fundamentally work the same, the difference from a user perspective (barring the actual technical differences between a $700 AP vs a $150 AP) is going to be the setup experience.
for example, won't necessarily support handling the shared SSIDs between the AP's or migration of the device to the best node for connectivity?
Correct. "High end" consumer routers (even old ones considered "high end" way back) may support "Access Point" mode but I can't think of one that supports wifi capability like a true AP. They are generally all MESH setups (wireless backhaul) and/or require they be on different channels and/or SSIDs to operate.
how do multiple AP's manage broadcasting the same SSID without clashing with each other?
It is a misconception that the same SSID and channels wont work together. This is only true of different networks. This causes problems when you are broadcasting in a neighborhood with many different wifi signals. This is not the case when using proper APs.
The answer I eluded too.
Congrats, you now have proper wifi that supports wifi ROAMING (IEEE 802.11r/k/v) it looks a lot like "mesh" on paper without the catastrophe.
when APs are used a "controller" be it an app or device always on or not (APs can communicate with one another) a single SSID, pass phrase, channel settings etc etc etc etc are shared between them. However each AP keeps track of what device is connected too it and their respective signal strengths. Using the protocols above APs have the ability to associate and disassociate devices at will allowing them to wirelessly "roam" between access points. They handle this between themselves using said protocols. Since all other settings are equal the device doesnt know the difference.
On really old equipment that doesnt support any of the roaming protocols, you see this as a temporary drop in connectivity as one AP drops you and the other picks you up.
This is how places like walmart, or starbucks, or malls, or schools do it. Conveniently, APs also give you the ability to broadcast multiple SSIDs (different names channels etc) this is how for example doctors offices or hospitals can have "Staff" and "guest" networks.
I'm going to take a shower and play video games hope that helps