I have no experience with liver transplant but I did have a large liver resection done in January 2018. It was a rough recovery and still ongoing. I do think it is amazong and selfless of what you're thinking of doing. Giving someone a new lease on life.
First 2-3 wks no driving is the Dr. Recommendation. Reality it will likely be a bit longer as of moving side to side to look out both ways will be painful and restricted.
I'm a non drinker and non smoker. Was in pretty good shape at 42, walked 2-4 miles, could run 2mi and stayed active playing basketball with my kids etc.
Energy gets zapped out while growing your liver, I'm talking aboit narcolepsy type sleep. Still get fatigued/drained.
Key to recovery is prior to surgery walk/run/swim. Increase your cardio and your leg muscles, these will help you displace the strain on abdominal muscles when doing simple things like going to the bathroom, getting in and out of bed, brushing teeth (do it slowly it will hurt) etc. Stay on top of your meds, don't let the pain creep in bc it's harder to control after.

Be positive, I could do some computer work early on, but first week or so you'll be pretty drugged up. Make sure you do your therapy and as soon as they say you need to get up and move, push through that pain. Staying Still and in bed will only make it worse. Within a week i was back to walking half a mile (with someone next to me).
Most important take your time, listen to your body and Drs.