Why is D.C.’s nonvoting delegate allowed to participate in official business in the House of Representatives, but D.C.’s shadow senators aren’t allowed to participate in the official business of the Senate?
You’re confusing the District’s mostly pointless elected representative with its entirely pointless ones.
While Del. Eleanor Holmes Norton can serve on House committees, she’s denied a vote on full bills (and on virtually all business on the House floor when Republicans are in charge, as they are now). The District’s shadow senators and shadow representative, on the other hand, are unpaid lobbyists elected to push for D.C. statehood—but they’re essentially a figment of the District’s imagination as far as the actual rules of Congress are concerned. The District tried to get a delegatelike representative in the Senate in the ’70s, but the senators weren’t having it. Aside from a few privileges (access to the Senate dining room!), the shadow delegation isn’t recognized as a real thing outside of their basement offices in the Wilson Building.