Dart

Nothing interesting here, just did it all explicitly. I might try something different in Uiua later.

solve(List lines, {int age = 2}) {
  var grid = lines.map((e) => e.split('')).toList();
  var gals = [
    for (var r in grid.indices())
      for (var c in grid[r].indices().where((c) => grid[r][c] == '#')) (r, c)
  ];
  for (var row in grid.indices(step: -1)) {
    if (!grid[row].contains('#')) {
      gals = gals
          .map((e) => ((e.$1 > row) ? e.$1 + age - 1 : e.$1, e.$2))
          .toList();
    }
  }
  for (var col in grid.first.indices(step: -1)) {
    if (grid.every((r) => r[col] == '.')) {
      gals = gals
          .map((e) => (e.$1, (e.$2 > col) ? e.$2 + age - 1 : e.$2))
          .toList();
    }
  }
  var dists = [
    for (var ix1 in gals.indices())
      for (var ix2 in (ix1 + 1).to(gals.length))
        (gals[ix1].$1 - gals[ix2].$1).abs() +
            (gals[ix1].$2 - gals[ix2].$2).abs()
  ];
  return dists.sum;
}

part1(List lines) => solve(lines);
part2(List lines) => solve(lines, age: 1000000);