The beaker for the pump takes 2 slots so that's 240v. The wire coming from the well has 3 wires. Red yellow and black. Well casing is 6 inch steel. At least above ground it is. The wire coming from the pump goes to a franklin electric box. Looks like a capacitor inside. Date code in there is 1996. Could that mean the pump is also franklin and the myers tag is from an old one?
In 1996 most pumps from the various makers had motors from Franklin. So you can't tell. Pumps from then were generally better than now, in the opinion of many.
The control box probably has a model number on it. That could tell you what HP motor that box was made to be used with. That is useful.
Note that the start capacitor has a limited life. They are non-polarized aluminum electrolytic capacitors, if that means something to you. If it doesn't, it is not worth researching. Just know those capacitors have a limited life. Replacing that now would probably be a good idea. That capacitor is only used during starting, but you are doing a bunch of starting right now.
Some control boxes have two capacitors. Most don't.
If you put in that pside-kick, I would put a 200 PSI gauge on its input line. That is not common, but I would want one myself. 200 PSI water pressure gauges are cheap and widely available. 1/4 NPT is the common thread size.