Touch Bar on my MBP isn't context-aware I have a 2020 MBP 13&quot; running macOS Big Sur 11.1 Beta.
The Touch Bar no longer shows icons relative to the active app - for example, when using Safari I'd expect to see Safari-specific actions. Mine just shows the default set (brightness, mission control, media controls, etc).
It definitely showed app-specific actions previously - I'd expect to see them for Safari, Pages, Numbers, PhpStorm etc. No idea when this stopped.
I've tried resetting it to the defaults in System Preferences, but it's not the defaults that are the issue - it's when in an application.
It took me a while to solve this, but the solution was:

Open System Preferences
Open 'Keyboard'
Change 'Touch Bar shows' to 'App Controls'

I'm not sure how this had been changed, but it had been set to 'Expanded Control Strip'