I think I’ve cracked it. Following the tutorial and using the mic-into-the-phones trick, it seems to have worked. I went through it once and it all lined up perfectly. SO I ran another few tests and every time I’d recorded the mic in the headphones it came out perfectly aligned.
I just now did it again and both tracks perfectly aligned with each other. It’s rather thrilling to see and hear.
So is that it? Do I delete the test results? Is this a one time thing, is the latency issue resolved forever? Can I now overdub without worrying about latency? Do I have to run a latency test before I record the next rhythm track? Nervous minds very much need to know these things.

Do I have to run a latency test before I record the next rhythm track?
No. The rhythm track is the one track that doesn’t need testing. It’s the master to which all others have to match. You might check the second track, the one you’re playing with the rhythm track. You don’t have to set up for the whole thing. Just put a click track lead-in at the beginning and play something that is intended to match such as rim shot or actual countdown in words. You can cut this off later in editing.
Congratulations. As long as you don’t change that “latency” setting and your computer doesn’t overload or slow down, you should be good to go. A note that during overdubbing, the computer has to record new work and play your backing, rhythm, and accompaniment tracks at the exact same time. This is not a good time to have the computer also calculating gross business receipts and executing a Photoshop Gaussian Blur. Or connecting to the intertnet.
A reality check is in order. You can check this as often as you like, but surgical accuracy isn’t needed. “Close enough for Jazz” is a thing and as someone once told me, what are the chances of all the instruments in the orchestra starting at the exact same time?
Koz
play your backing, rhythm, and accompaniment tracks
In case that went by quickly, you only need the backing track once. After that you can play as many tracks as you wish into your headphones. This is the process that lets you sing harmony to yourself. Set the tracks that play with the SOLO and MUTE buttons. If MUTE and SOLO don’t seem to work right, you can change the behavior with Audacity > Preferences > Tracks > Track Behavior > Solo Button:
Koz
I see you made a distinction between the click track and the rhythm track. Some people don’t. The second track is needs to match and if you’re performing live, remember that human reaction time is a thing, too.
Koz