I probably won't come up with anything you haven't thought of...but I won't let that stop me from responding!!
I have been tired most of my life due to PTSD. When I would get a new job, I would be distracted from my fatigue but once it became rote, I became more aware again. I don't know if this happened to you.
Best to get a check up and see what's what, including blood test, adrenals, etc. You might have anemia or...?
If you check out okay there, then you have to look at food and rest and exercise. For me sleep is hard to come by but I can patch together sufficient so Im not deprived. Even if I can't, I make sure to walk every day. That is the best thing I do for my fatigue currently since I do eat right. Even if I had little to no sleep I can still take a half hour moderate walk and feel better with renewed energy.
Congrats on the new job!