It is varying between single and multiple bars, like searching for a WiFi signal.
... and that is exactly what it is doing.
Typically, once a SSID is chosen, the WiFi icon on the Menu bar is supposed to be solid...
In theory, yes, but it is not always the case, especially if there is any form of Wi-Fi interference present in the nearby area. Also, if you happen to have multiple wireless access points in your current network configuration, your MBP may be attempting to roam to a base station with a stronger signal. iOS clients have a similar experience with roaming.
...but the adapter continues searching for better APs or a better signal as shown with the Alt+Click where it varies between 'WiFi:Looking for Networks' and 'WiFi: On' . This is what I have normally seen for years.
Yep, and we have seen this to be more of the "standard" with the later versions of OS X or macOS.
You can do a bit more "investigating" to see just how stable your Wi-Fi network is from the perspective of your MBP by using its built-in Wireless Diagnostics utility. I will get to that in a moment, but I want to take a look at your Wi-Fi values that you posted first to get some clues.
Ok, back to using Wireless Diagnostics. What we would be interested in is the SNR value over time. Specifically we would want it to not vary much. As you know, you can access this utility via Option-clicking on the Wi-Fi icon on the OS X menu bar. We would want to use the Performance tab. If there is significant amount of variation, the culprit can either be Wi-Fi interference or a faulty base station.