I have applied for renewal of my driving license in Bangalore last year during Covid first wave and uploaded all documents as required to Parivahan site. But did not get the slot for document verification yet. Nor the site provides option to book. How do I proceed now given that current wave of Covid and my license has already expired?

In fact your license has validity till June 30. You can renew online with eye test certificate and form 1/1A.  And send the documents by post to RT office if it is necessary there in Karnataka.