Does it give the courts the right to adjudicate legal disputes?
The constitution explicitly gives Congress, not courts, the authority to act as a final
judicial tribunal on disputes relating to election of house members. It's carved out from any powers given to courts.
Courts having any say at all in Congressional election disputes was only established in 1972 when SCOTUS overturned the District Court in
Roudebush v. Hartke and ruled courts have some authority provided they don't interfere with the final exclusive jurisdiction of Congress. There is much
debate how to interpret Roudebush v. Hartke, but notably, in his partial dissent, Douglas writes Congress still has authority to subpoena ballots to physically prevent a judicially ordered recount.
Claiming the courts are a more appropriate venue than Congress is simple ignorance if not political dishonesty. I'd actually be surprised if you still dispute it.