Hello alessioBliss3t,
We understand you're having some issues with your MacBook Pro's Touch Bar display flickering, and showing colored vertical bands after upgrading to macOS Big Sur. We definitely get wanting to have full functionality of your MacBook Pro's Touch Bar, so we're more than happy to help see if we can isolate what's causing this.
To begin, do the vertical bars/flickering issues occur no matter how the Touch Bar is set up? For example, if you customize the Touch Bar, does the issue continue? Let's try doing so, using the steps here (under the "Customize the Control Strip" section):
Use the Touch Bar on MacBook Pro
If the issue persists, let's try having you boot into safe mode: this will help us to isolate if this could be occurring due to certain software that's loading up with your Mac. Please review the following article, starting with the "How to use safe mode: Intel processor" section:
How to use safe mode on your Mac
From there, should you continue to experience any issues, let's have you try resetting your System Management Controller. The system management controller is responsible for managing behaviors related to these features: power, fans, sensors, keyboard backlighting, etc. Please review the following article, under the "Notebook computers with a nonremovable battery" section for instructions on how to reset your Mac's SMC:
How to reset the SMC of your Mac
We're confident that these steps should help resolve that you're experiencing: in the event that you do continue to experience issues, we may need to get your device physically inspected. Please check the following link for information on how to get your Mac inspected by Apple Support:
Contact Apple Support
Cheers!