I'm not much into visual media, so I can only come up with a few examples of 'sleep' devices:
Star Trek's "Space Seed" - 200 years in sublight stasis, no mention of speed or distance. Could be 0.5c for all we know. 100 ly at Enterprise's warp 6 cruising speed would take about 4 months, which seems not unreasonable.
The movie "Alien" - stasis, but seemingly with FTL given the times and distances involved. (https://avp.fandom.com/wiki/LV-223 says it was a 2 year voyage to the moon LV-223 in Prometheus.)
Star Trek's "Space Seed" - 200 years in sublight stasis, no mention of speed or distance. Could be 0.5c for all we know. 100 ly at Enterprise's warp 6 cruising speed would take about 4 months, which seems not unreasonable.
The movie "Alien" - stasis, but seemingly with FTL given the times and distances involved. (https://avp.fandom.com/wiki/LV-223 says it was a 2 year voyage to the moon LV-223 in Prometheus.)
The TV series "Red Dwarf" - sublight, though it did break the light barrier once. Science in general is only relevant for comedic effect. https://www.ganymede.tv/2004/04/the-science-of-red-dwarf/ .
None of these seem to be characterized as "it takes you 150 years of travel at light speed to get to a place that is 150 light years away".
Which one am I missing?