I'd just go with what this dude started. It's a little late to worry about inspectors now, LOL
2" PVC underground is standard and gives you room to grow. 6/6/8/10 isn't bad.
Do keep grounds and neutrals separate in that subpanel. Do put in a ground rod (maybe 2) and land it to the ground bar, I used to run a #4 for ground rods. Do not install the main bonding jumper if the subpanel comes with one. Someone would view that setup as being feeders to a subpanel in a separate building requiring ground rods instead of that being just a branch wiring circuit (IMHO). I wouldn't go much more that a couple of 20A circuits out of that subpanel if at all possible, and of course on opposite legs.
Not sure what the plan is to go from 2" to 1" before entering the panel. My first impulse would be to mount something like a NEMA3 4x4x12 to transition through but /shrug. Curious what your dude would want to do.
Drunk Erronius Wednesdays YOLO!!
After I did this thought of a bit cheaper way. Twas a long time ago, before this stuff and convenient shopping. But would have went out the back with 1 and LB out the side with the other one instead of this raceway.
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