Nim

Runtime: 30-40 ms
I'm not very experienced with recursion and memoization, so this took me quite a while.

Edit: slightly better version

template splitNum(numStr: string): seq[int] =
  @[parseInt(numStr[0..<numStr.len div 2]), parseInt(numStr[numStr.len div 2..^1])]

template applyRule(stone: int): seq[int] =
  if stone == 0: @[1]
  else:
    let numStr = $stone
    if numStr.len mod 2 == 0: splitNum(numStr)
    else: @[stone * 2024]

proc memRule(st: int): seq[int] =
  var memo {.global.}: Table[int, seq[int]]
  if st in memo: return memo[st]
  result = st.applyRule
  memo[st] = result

proc countAfter(stone: int, targetBlinks: int): int =
  var memo {.global.}: Table[(int, int), int]
  if (stone,targetBlinks) in memo: return memo[(stone,targetBlinks)]

  if targetBlinks == 0: return 1
  for st in memRule(stone):
    result += st.countAfter(targetBlinks - 1)
  memo[(stone,targetBlinks)] = result

proc solve(input: string): AOCSolution[int, int] =
  for stone in input.split.map(parseInt):
    result.part1 += stone.countAfter(25)
    result.part2 += stone.countAfter(75)

Codeberg repo