Does anyone have problems with their MacBook Pro 13 inch (2020) with battery drainage and overheating?

Probably you have taken these steps already. Give it another try.

Update the software on your Mac,

    Update may come with bug fixes.

    https://support.apple.com/en-us/HT201541

Reset  SMC:   How to reset the SMC of your Mac - Apple Support   Choose the appropriate method.

Quote:

Resetting the system management controller (SMC) can resolve certain issues related to power, battery, fans, and other features.

Startup in Safe mode. https://support.apple.com/en-gb/HT201262 Choose the appropriate method.

To leave Safe Mode, choose “Restart” at the bottom.

Quote:

     Safe mode prevents your Mac from loading certain software when it starts up, including login items, 

     system extensions not required by macOS,

     and fonts not installed by macOS. It  also does a basic check of your startup disk, 

     similar to using First Aid in Disk Utility. 

     And it deletes some system caches, including font caches and the kernel cache, 

     which will be created again automatically as needed.

mac1803 wrote:

Recently experienced bad overheating, loud whirring on the fan and battery drainage. Total battery utilisation barely meets 2 hours, dropped from 83% to 5%. This is extremely puzzling since its a lap top instead of a phone.

I'd like to get some feedback regarding this matter. I just had it brought back from the service centre, however, was informed that there is no problem on the battery and all conditions were still fine.

Keep your Mac notebook within acceptable operating temperatures

https://support.apple.com/en-us/HT201640

Maximizing Battery Life and Lifespan

Batteries - Maximizing Performance - Apple

About battery health management in Mac notebooks— introduced with macOS10.15.5

https://support.apple.com/en-us/HT211094