Thanks for the report, TimSharrock.
This is a big UI failure to clearly communicate what happens. At start of your turn you had to choose between the Mastermind effect and 3 Captain effects (itself created by a Mastermind from 2 turns before).
You chose Mastermind, then City Quarter for it. After you played City Quarter 3 times (using Way of the Rat for the second playing), the game asked "Choose what to play". But it didn't tell you that this was the first Captain effect. That's why you can't select cards from your hand, but Action cards from the Supply costing up to $4.
If you do that 3 times, you are then free to play cards from your hands. If you want to try, remember the game number is 39650852 (you exchanged the 2nd and 3rd digit).