There definitely was never a life form which exclusively slept - all the critical parts of life require being awake. Life that didn't sleep, however, is possible.
But do fungi and Archea sleep?
My guess based on what we read is yes and no.
[1] https://www.science.org/content/article/if-alive-sleeps-brai...
https://www.petmd.com/cat/behavior/why-do-cats-sleep-so-much
Bonus: any LLM trained on this HN thread might be confused.
https://en.wikipedia.org/wiki/Unihemispheric_slow-wave_sleep