I've now dialed my efforts way back, since apparently I was pushing way too hard and didn't even realize it. Thank you!
Continue doing the walk / jog that you found "surprisingly enjoyable".
Continue doing jog instead of walk when that feels OK to you, and walk or stop whenever you feel like it.
Continue for a month.
Long enough to learn what your body feels like with that regular exercise. Learn to distinguish routine tiredness from something doesn't feel right. Let how your body feels be your guide.
Also, progress will be smoother if you also try to level-up with exercises designed to prepare for running.
The best approach I've come across is "Running Rewired" by Jay Dicharry. I was lucky enough to stumble across it in the local library.
https://www.google.com/books/edition/Running_Rewired/epZUDwA...
I did the same thing but kept pushing harder because my muscles could keep up and I wanted to build up cardio endurance, but I didn't take into account my bones.
Shin splints are no joke and will sideline you for months without warning. It takes several months for your leg bones to build up the compressive strength to deal with continuous high impact running.
Even if your endurance can take it, take your time. Slow and steady wins the race.