The steam client itself may have some broken or damaged files and hence may be leading to VAC was unable to verify the game session error.
To fix this,
Press the key combination Windows + R. Run… dialogue box shall appear.
2. Type cmd in there and open the command prompt.
3. In the command prompt, copy and paste “C:\Program Files (x86)\Steam\bin\SteamService.exe /repair” without the included quotes and press enter.
4. If the path to the SteamService.exe is different in your system, replace the path with the path of your SteamService.exe.