Inspired by https://mapstodon.space/@bogind/109558968869019746 and listening to https://www.youtube.com/watch?v=AdyAF9M3XVw on repeat thanks to https://ruby.social/@halfbyte/109558803178815394 I made:

This was the final expression (with lots of opportunity to improve):

with_variable(
  'point_at_top_of_canvas',
  densify_by_count(
    make_line(
      point_n( @map_extent, 3),  -- no idea if these indexes are stable
      point_n( @map_extent, 4)
    ),
    42  -- number of trajectories
  ),
  collect_geometries(
    array_foreach(
      generate_series(1, num_points(@point_at_top_of_canvas)),
      with_variable(
        'point_n_of_top_line',
        point_n(@point_at_top_of_canvas, @element),
        point_n(
          wave_randomized(
            make_line(
              @point_n_of_top_line,
              -- make it at least touch the bottom of the canvas:
              translate(@point_n_of_top_line, 0, -@map_extent_height)
            ),
            -- fairly stupid frequency and wavelength but hey, works in any crs
            1, @map_extent_width/5,
            1, @map_extent_width/100,
            seed:=@element  -- stable waves \o/
          ),
          floor(epoch(now())%10000/50)  -- TODO make it loop around according to num_points of each line
        )
      )
    )
  )
)

Use it on an empty polygon layer with an inverted polygon style and set it to refresh at a high interval (0.01s?). Or use this QGIS project (I included some intermediate steps of the style as layer styles if you want to learn about this kind of stuff):