Dart

~~I'm cheating a bit by posting this as it does take 11s for the full part 2 solution, but having tracked down and eliminated the excessively long path for part 1, I can't be bothered to do it again for part 2.~~

I'm an idiot. Avoiding recursively adding the same points to the seen set dropped total runtime to a hair under 0.5s, so line-seconds are around 35.

Map, Set>> seen = {};

Map fire(List> grid, Point here, Point dir) {
  seen = {};
  return _fire(grid, here, dir);
}

Map, Set>> _fire(
    List> grid, Point here, Point dir) {
  while (true) {
    here += dir;
    if (!here.x.between(0, grid.first.length - 1) ||
        !here.y.between(0, grid.length - 1)) {
      return seen;
    }
    if (seen[here]?.contains(dir) ?? false) return seen;
    seen[here] = (seen[here] ?? >{})..add(dir);

    Point split() {
      _fire(grid, here, Point(-dir.y, -dir.x));
      return Point(dir.y, dir.x);
    }

    dir = switch (grid[here.y][here.x]) {
      '/' => Point(-dir.y, -dir.x),
      r'\' => Point(dir.y, dir.x),
      '|' => (dir.x.abs() == 1) ? split() : dir,
      '-' => (dir.y.abs() == 1) ? split() : dir,
      _ => dir,
    };
  }
}

parse(List lines) => lines.map((e) => e.split('').toList()).toList();

part1(List lines) =>
    fire(parse(lines), Point(-1, 0), Point(1, 0)).length;

part2(List lines) {
  var grid = parse(lines);
  var ret = 0.to(grid.length).fold(
      0,
      (s, t) => [
            s,
            fire(grid, Point(-1, t), Point(1, 0)).length,
            fire(grid, Point(grid.first.length, t), Point(-1, 0)).length
          ].max);
  return 0.to(grid.first.length).fold(
      ret,
      (s, t) => [
            s,
            fire(grid, Point(t, -1), Point(0, 1)).length,
            fire(grid, Point(t, grid.length), Point(0, -1)).length
          ].max);
}