The grounding should be fine...
What you're doing here is running multiple circuits (the feeder out to the subpanel and the branch circuits back) through a single raceway with a single equipment grounding conductor, as implicitly provided for in NEC 250.122(C):
(C) Multiple Circuits. Where a single equipment grounding conductor is run with multiple circuits in the same
raceway, cable, or cable tray, it shall be sized for the largest
overcurrent device protecting conductors in the raceway,
cable, or cable tray. Equipment grounding conductors installed in cable trays shall meet the minimum requirements
This, plus the fact that a single EGC can branch into multiple EGCs downstream of a panel when a multi-circuit raceway splits into individual circuits, means that you are fine on the grounding standpoint.
However, that poor, sweltering feeder cable isn't!
That feeder cable, on the other hand, is very not-fine. Putting 18 current-carrying wires (8 branch circuit hots and neutrals each, as well as the 2 feeder hots) into a single raceway forces a whopping 50% derate on the conductors (as per Table 310.15(B)(3)(a)), and 30" is a bit too long for the short-raceway provisions in 310.15(B)(3)(a) point 2, which are limited to raceways 24" or shorter. This means that your 2/2/2/4 SE cable is limited to 50A(!) and your 12AWG branch circuit wires can only handle 15A.
Fixing this would require re-running the middle panel's feeder and returning branch circuits using properly sized wires -- the branch-circuit wires would need to be bumped up to 10AWG, and the feeder hot wires would need to be bumped up to 1/0AWG (although a smaller neutral could be acceptable here, depending on the amount of unbalanced load anticipated in the subpanel). With your 1.5" EMT, the 10AWG THHN branch circuit wires (at 13.61mm2 of fill each), and compact stranded XHHW-2 singles for the feeder hot conductors, this leaves you with 422.96mm2 of fill used out of 526mm2 usable, before accounting for the neutral -- a full-size 1/0AWG neutral takes up another 102.6mm2 of fill, pushing you to the very limit of what that conduit can handle.
As a result, I'd recommend replacing it with 2" EMT to provide room for growth, or running two more EMTs (1/2" will do, with 72mm2 used vs 78mm2 usable) to allow the use of 12AWG wire for the branch circuits coming back via the new conduits. (Adding the extra conduits doesn't change the grounding logic from above at all, by the way.)