From personal experience, after lucid dreaming (not semi-lucid) I feel like a vulcano. Seriously, I've never experience something as energising as lucid dreaming. I still remember the first time I had my first one: I felt like I was overloaded by electricity, one of the best sensation of my life. On the other hand, when the lucid dream transitions to semi-lucid and no-lucid, then I usually feel pretty tired.

These days when I lucid dream it often wakes me up very soon after I realise I’m lucid dreaming. So, definitely less rested.

When I was a kid I could just live in my dream for hours. Seem to have lost that ability.

They can give an incredible energy boost and moodlift in my experience, but if feeling physically more rested is the goal, then I wouldn't spend the time & effort to try to induce lucid dreams.

From someone that has chronic lucid dreams, I heard they were not over time.