In my home LAN, I have two access points, each of which has 2.4 and 5GHz bands. They are all configured for the same SSID and the same password.
As I understand it, when the phone connects to the network, it will select the one with the strongest signal. It will then stick with that AP until it decides that the connection is bad (lost the connection, too much interference, etc.) and it will then select another.
What it will not do is automatically switch from a good quality signal to one that is “better” - that’s one of the key benefits to using mesh networks. Without a mesh, you can do what you’re doing now (manually select a different SSID when you want to switch) or you can do what I do and manually flap Wi-Fi off/on, which will cause the device to seek out the strongest signal at that time.