Did I "cook" my batter tender by not unplugging it when I ran my T ?
Probably not but it depends on the "smarts" of your battery tender. It should sense the voltage increase if you have a generator. Now if you drove off with it still plugged into the wall, that's another story.
I can relate to the plugged into the wall comment.
I now have a note that I tape to the steering wheel, BATTERY CHARGER !!!
No worries. Battery chargers have diodes in them that prevent current from feeding back to the charger (tender).
I leave my trickle charger permanently connected with the AC plug hanging out. When I get back from a long trip, I just connect an extension cord to it. Working for 3 years so far.
It depends upon the specific battery tender/charger.
I blew one on my old pickup when I started it while the charger was on. It was supposed to be protected. I think it was the starter's power draw that may have killed it.
I also blew one using it for a rust removal power source.
Drive carefully, and enjoy, W2