I've recently returned to tennis after a 15 year or so absence.
My serve is still bad, but it was never a weapon (retooling it with a coach now). It took me about a month of regular playing (three times a week) to get my forehand back, but my backhand was on from from day 1, more or less. It was always my stronger shot.
The funny thing is, i find that when i'm outstretched running for a forehand or am in the heat of a tough rally i will pull off shots as if I had never stopped playing tennis! I understand the over-thinking bit you talked about.
My movement was really bad during the first month as my fitness wasn't at the level which allows me to execute my game. I had never been so aware of my joints and weight before! There are certain stresses you feel on a tennis court that you don't in the gym or out running/cycling. Once I got my fitness back up, regular tennis helped as did some cycling/running, my game really improved and I can safely say that I could probably beat my 15-year-old-younger self in a best of 5 match now.
Stick with it, but make sure you give yourself enough days rest between practice sessions and matches especially during the first couple of months as your body is probably not used to the stress of tennis. the last thing you want is an injury on the court that will put your game back even longer.
It's such a fun sport, i wish i had never stopped playing.
Disclaimer: I'm NOT a coach...
Real tennis: https://www.youtube.com/watch?v=yDqnkLJ9BtM