Your allowed to take small backpacks, purses etc… into most places in DC right ? The monument, capitol , museums etc…
I think the only place your not allowed a bag is the White House ?
Rules can vary, and things can change. There might even be a bag allowed at one place for a certain size but not allowed at another site.
I’d recommend checking the official sites for the places you’re planning on visiting.
Here’s the Washington Monument site to get you started:
Plus they rummage through your bag at some museums that don't use metal detectors. So less stuff is better.
Bringing a backpack is not a problem. Small wait at some places but usually under 2 mins to get it checked. In my experience it's usually less of a rummage and more of a 5 second look.
Backpacks have become a hindrance. Some places allow and others make an issue out of them. I have less trouble with dogs than with a backpack these days.
Backpacks can whack art and people when on the back so they are an issue. A hand carried bag or side bag like a purse or sling bag, less so.
I guess people are "over covid" but personally I dislike people or a multiused stick touching the inside of my purse.