Why does my Apple Watch count sleep while I'm awake?

I'm afraid, this can not be stopped. The watch is detecting a nap. Happens to me as well on my Ultra 2, same scenario, reading and sitting still at a table:

You should let Apple know directly that this has to be improved by using the Feedback link.

This is the only way to make Apple Techs aware of issues.

Feedback - Apple Watch - Apple

Here's a way to stop this behavior, with two following steps:

1. Enable sleep tracking manually when you're actually going to bed by setting the Sleep Focus mode
2. Turn Off sleep tracking outside of bedtime: On your iPhone, open the Watch app, select "Sleep", then toggle off "Track Sleep with Apple Watch".

This way, when you're ready to sleep, turn on the Sleep Focus manually (via the control center on your watch or phone), but your Apple Watch won't log sleep data unless you re-enable tracking. This should stop it from counting daytime activity as sleep.

For the time you're reading and don't want to be disturbed, I would suggest using the Do-Not-Disturb focus mode.