I've experimented with this a fair bit, but my experience so far is: when I ramp up activity I see improvement in sleep, but once it becomes normal it doesn't help much. I also occasionally run into really annoying situations where I'll do some pretty heavy lifting during the day, then go to sleep knowing how important it will be for me to get rest that night—which creates the kind of self-awareness trap described above and I lay there for hours super tired but also kind of wired, tossing and turning.
Most of my experience with this has been relatively high intensity over ~1.5hrs though, not full days of physical activity (like I had with jobs in the past, landscaping or stocking groceries etc.)—but I don't have that much time to dedicate to it with the desk work I'm doing now.
Anecdotally, I find even dedicated heavy lifting (1-1.5 hours) does not improve my sleep but similar durations of high-intensity cardio (45 minutes+) heavily improve my sleep even comparing for differing work-related stress baselines. I alternate lifts/HIIT,Tabata and do this regularly (2+ years of 5-6/week workouts) and still have reduced sleep latency times compared to before dedicated regular work-outs. My job is 100% sedentary desk job as well. Dunno if that helps.
We’re built to move and are surprised that sitting in a chair all day leaves us feeling restless and on edge. Kinda silly when you think about it.
When I get enough exercise, sleep is easy. You close your eyes, are bored for 5 minutes, and then you’re asleep.
Without daily exercise? Forget about it. Tossing and turning, tapping my feet all night, can’t get settled, every little thing an annoyance.