I took a very similar approach to parts a and b, with the difference that i was too lazy to do titling in each direction, and wanted to abuse regex so Instead i always titled up and rotated, which given my method of tilting up and rotating had some satisfying cancelling of transpose operations: https://github.com/zogwarg/advent-of-code/blob/main/2023/jq/14-b.jq

# Relevant portion
# oneCycle expects an array, of array of chars (3x3 eg: [[".","#","."],[".",".","."],["O",".","#"]])
def oneCycle:
  # Tilt UP          = T . MAP(scan) . T
  # Rotate           = T . MAP(reverse)
  # Titl UP . Rotate = T . MAP(scan) . Map(reverse) | T . T = Identity
  def tilt_up_rotate:
      transpose          # Gets subgroups    # Within each group,
                         # starring with "#" # In order 1 "#", x "O", y "." 
    | map( ("#" + add) | [ scan("#[^#]*")    | ["#", scan("O"), scan("\\.")] ] | add[1:])
    | map(reverse)
  ;
  # Tilt   North,            West,           South,            East
  tilt_up_rotate | tilt_up_rotate | tilt_up_rotate | tilt_up_rotate
;

JQ does allow some nice sortcuts sometimes, again transpose is nice to have.