Use a fat conduit and appropriately sized THHNs instead

Direct-bury wire (UF) is vulnerable to excavation damage and difficult to upgrade if you want more power at the shed later. Hence, it's better to slap a fat PVC conduit in now while you're digging the trench for the first time -- conduit's cheap compared to the cost of renting a trencher. Inside the conduit, you'll use 3 THHNs of appropriate size and color for 2 hots and 1 neutral (voltage drop control will likely mandate a larger size than the 10AWG minimum you were thinking of) as well as an appropriately sized bare copper ground (10AWG for a 30A feeder, 8AWG for a bigger feeder up to 100A) wire.

Don't skimp on the subpanel either

Buying small electrical panels is penny-wise and pound foolish as a larger panel now is always going to be cheaper than upgrading later. I'd recommend a 100A/24slot subpanel at a minimum here (you can always feed a large subpanel with a small feeder, just not the other way around -- remember that the protecting breaker must be the bottleneck so it can keep you safe from overloads). You'll also need a main device (it can be a breaker or a molded-case switch) at the subpanel to serve as a disconnect switch for the shed in addition to the breaker in the main panel protecting the feeder. (That's so you, or the FD, can shut power to the shed off quickly if it catches on fire -- "firemen don't deal with wires" after all.)

Last but not least, you'll need a ground electrode (Ufer ground if you haven't poured the foundation yet, rod if you have and need something you can put in now) in addition to the grounding wire -- the grounding wire provides a fault path (safety drain) back to the source while the ground electrode dissipates built-up static charges, induced voltages from lightning, and the likes. Don't forget to pull the bonding strap or screw from the subpanel when you put it in!

Yes, it's permitted in Article 225. But...

If exposed to temperature extremes, you must provide "expansion fittings" per 300.7 and as a general rule, running it along the side of a building wall usually qualifies as exposure to temperature extremes.

Article 352 ALL pertains to using PVC conduit, but there are a couple of things to note: A) 352.12 says that you can't use it where subject to physical damage, but... B) 352.10 had just said that you CAN use it. The subtle and often missed detail is that 352.10 has a note explaining that SCHEDULE 80 PVC is allowed for use where physical damage is probable. If you are unsure of how your situation applies, just use Schedule 80.