Nim

Part 1: there’s no need to simulate each step, final position for each robot is
(position + velocity * iterations) modulo grid
Part 2: I solved it interactively: Maybe I just got lucky, but my input has certain pattern: after 99th iteration every 101st iteration looking very different from other. I printed first couple hundred iterations, noticed a pattern and started looking only at “interesting” grids. It took 7371 iterations (I only had to check 72 manually) to reach an easter egg.

type
  Vec2 = tuple[x,y: int]
  Robot = object
    pos, vel: Vec2

var
  GridRows = 101
  GridCols = 103

proc examine(robots: seq[Robot]) =
  for y in 0..<GridCols:
    for x in 0..<GridRows:
      let c = robots.countIt(it.pos == (x, y))
      stdout.write if c == 0: '.' else: char('0'.ord + c)
    stdout.write '\n'
    stdout.flushFile()

proc solve(input: string): AOCSolution[int, int] =
  var robots: seq[Robot]
  for line in input.splitLines():
    let parts = line.split({' ',',','='})
    robots.add Robot(pos: (parts[1].parseInt,parts[2].parseInt),
                     vel: (parts[4].parseInt,parts[5].parseInt))

  block p1:
    var quads: array[4, int]
    for robot in robots:
      let
        newX = (robot.pos.x + robot.vel.x * 100).euclmod GridRows
        newY = (robot.pos.y + robot.vel.y * 100).euclmod GridCols
        relRow = cmp(newX, GridRows div 2)
        relCol = cmp(newY, GridCols div 2)
      if relRow == 0 or relCol == 0: continue
      inc quads[int(relCol>0)*2 + int(relRow>0)]

    result.part1 = quads.foldl(a*b)

  block p2:
    if GridRows != 101: break p2
    var interesting = 99
    var interval = 101

    var i = 0
    while true:
      for robot in robots.mitems:
        robot.pos.x = (robot.pos.x + robot.vel.x).euclmod GridRows
        robot.pos.y = (robot.pos.y + robot.vel.y).euclmod GridCols
      inc i

      if i == interesting:
        robots.examine()
        echo "Iteration #", i, "; Do you see an xmas tree?[N/y]"
        if stdin.readLine().normalize() == "y":
          result.part2 = i
          break
        interesting += interval

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