Welcome To...
In Solo Mode, when does the reshuffle happen and what gets shuffled?
The designers answered the timing and the shuffle in 2019.
Once, when the first City Plan is actually scored by you or the AAA, not when a Completed Plan card is merely drawn. Combine the discard pile with the rest of the deck and shuffle them together (do not put the discards on top). The AAA's own stack and Completed Plan cards that were drawn are not shuffled back. The reshuffle is intended: it gives you more time to score plans before the AAA.