You'll probably have snow on Mt Lemmon, Oracle ridge likely dicey. Once you descend back to the 4,000 - 3,000 range should be fine. Water likely no issue in January, with rain we have and are going to get this week. As far as resupply, the store in Summerhaven you may want to call for hours. Next opportunity is the ADOT yard at Kelvin (where 16 begins) you can order Old Time Pizza in Kearney and they deliver to the ADOT lot, there is also a water faucet there. Then, nothing until Queen Valley/Gold Canyon, where you have fast food and gas stations.
You said you have not ridden any of the AZT? A couple of musts...
Tubeless, tubeless, tubeless... Tubes are worthless in AZ. Carry an extensive flat kit, extra sealant, tire boot, and more sealant.
Try to avoid using water cached at trailheads. Hikers need that, they can't cover the distance a biker can between water sources.
The climb up Martinez canyon is longer and steeper than you think. Lots of H.A.B. here. There is now an AZ game and fish rainwater catchment about halfway between the Gila river and Picketpost mountain. It will have water.
Tell me a little about your bike setup you'll be riding...
Here are a couple of links you may find helpful with other details of your route.
https://bikepacking.com/event/arizona-trail-race-2022/
http://schillingsworth.blogspot.com/
AlMal