Only way out has been to use WhatsApp Web instead of actual app.
UPDATE: I must stand corrected on that - while pmset assertion has not been changed over updates in last few months, sleep is now possible while it was not before. No way to know if it is about WhatsApp update or has macOS 26.3 solved it.
One more update - but now from Meta - ruined this again. Now it is so bad that I can quit WhatsApp and all is fine... but then I wake computer up again and after that it won't go sleep even manually and when I check what is causing it - I see that WhatsApp is still running after it was quit and preventing any form of sleep. I threw it away and would not probably use it again. Web app does not have this problem.