The blue check isn't coveted by most, there's even a meme about it being a mark of shame. I really think people that don't use Twitter often overestimate the importance of blue check accounts. If anything, they are the butt of a lot of jokes/content vs creating it. I am interested in the new Twitter Blue, but actually don't want the checkmark, but think it needs more features.
That being said, a normal user shouldn't have the same mark as an official Microsoft or government account. A secondary mark make sense, especially imo if only other paid and verified accounts can see the mark (I would just make it a hollow verified icon vs it being a different color.) Then it creates a network "in crowd" effect (similar to the green v blue text bubbles.) You also need to pair that with better tools and features.