Why does my MacBook Pro freeze when the trackpad goes to sleep mode?

SOLVED for me.

This post helped me: 7625326

I suggested that the reason may be not a logic board fault, but a “contact disease”: i disconnected some cables while been cleaning the laptop first time.

So, i disassembled it again, cleaned carefully all the connectors with alcohol and slightly tightened logic board screws - and bingo! It works perfect. So i have maybe an old laptop, but with 2TB SSD and Big Sur onboard ))

The only thing annoying me - why hardware test haven't discovered the trouble?

Well, "Nobody's perfect" )))

Found similar issue: macbook pro freezes when mouse stops - Apple Community

Yes, i also tried to connect external mouse - the system stays alive while i moving the mouse or the trackpad.

But the result of discussion mentioned above is discouraging: it seems like a logic board issue. The only thing i can not understand - why it worked well for years until i disconnected a battery for a while?..

BDAqua wrote:

Are you running any VPN, Anti-Virus, or Cleaning apps?

Not at all, on new SSD Big Sur is just instlalled and clean, on old one OSX10.15 with no VPN, antiviruses (what is this??))) or cleaners (OSX do it itself quite good).

Will send EtreCheck report soon...

Here is it.