I'd upsize to 125A if I were in your shoes
Given the short length of your wire run (20-odd feet of SER should be sufficient), there's really not much reason to penny-pinch by using an odd-sized feeder; as a result, I'd go up to 125A as larger two-pole breakers require 4 spaces in the feeding panel instead of 2, and you won't be able to make full use of a 225A feeder and subpanel anyway, which is the next size larger as far as main lug panels go.
This means that you'll be using 1/0-1/0-1/0-2 aluminum SER cable instead of the 2-2-2-4 you were originally planning on, and a 125A feeder breaker instead of the (admittedly odd sized) 90A feeder breaker in your original plan. If conduit is called for (which isn't likely, given that the chances of something between studs being considered subject to physical damage are rather low), then you can use a 1.5" EMT with 3 1/0AWG aluminum wires inside it instead. In any case, the 75° column in the ampacity tables is what governs for feeders in realistic work, see 110.14(C) point 3 for details.
If you want to use a larger conduit, by the way, that is fine; IRC R602.6.1 would require strapping for a bore larger than 1.75" (50% of the 3.5" actual width of a 2x4 top plate) through the top plate of a load-bearing wall, but even that is not needed for a non-load-bearing partition.
You have the wrong panel picked out anyway
Given that your subpanel is in the same building as the panel feeding it, there is no need for your new subpanel to have a main breaker; furthermore, it's a Homeline, not a QO, so you'll have to keep that in mind when populating it with breakers since the two breaker types are very much not interchangeable!
With all of the above taken into account, and going for as many spaces as we can so you don't have to rip it out and replace it later, we can use a HOM3060L125PGC if you can find it, or a HOM2448L125PGC if the former is not available. Both of these panels support the full 125A capacity of the feeder I am suggesting, have main lugs (since a main breaker is not needed here), and come with factory-fitted ground bars (obviating the need to buy ground bar kits and install them).
Having a panel flush-mounted into an unfinished wall is fine, even if it looks odd
There is no Code issue with flush-mounting a panel into an unfinished or partially-finished wall; just keep in mind that it may be necessary to unmount and remount the panel when the wall is finished so that the outer portion of the panel cover fits correctly over the drywall. (This weighs against using conduit for the feeder, BTW.)
Last but not least: TORQUE ALL LUGS TO SPEC
There is one other thing you'll need to take into account, and that is that the set-screw type mechanical lugs used on circuit breakers and loadcenters need to be torqued to the values labeled on the breaker or loadcenter for that size wire in order to perform reliably over the long-haul. This was added to Code as a requirement with 110.4(D) in the 2017 NEC; even if your AHJ has not adopted the 2017 edition, using an inch-pound torque wrench and/or torque screwdriver to tighten the lugs to their specification torques is a good idea anyway, lest your electrical system lose you the race!