It is not unconstitutional on its face, but like a lot of other laws, it could be applied unconstitutionally. In this case, an attempt to use it to remove a sitting President from office would be unconstitutional. The Constitutionally correct legal remedy for treason by the President would be three steps: 1) The House would impeach the President for treason, 2) the Senate would vote to convict him by a 2/3 majority, and then 3) the now former President could then (and only then) be prosecuted criminally for treason under 18 U.S.C. Section 2381.
The idea that you could just bypass the entire Constitutionally-mandated impeachment procedure simply by some lowly federal prosecutor bringing charges against a sitting President, and then having him convicted in any one of nearly 700 federal district courts around the country, is absolutely absurd.
Just think how easy it would be for a single prosecutor in D.C. to convict a conservative Republican President of treason (they might have tried it against Trump if it was possible) and then just give him the boot. There isn't any hint anywhere in the Constitution that is permitted, nor is there anything in Supreme Court caselaw suggesting that a criminal conviction of any kind results in the removal of a President. You want him out? Impeach him, then prosecute him criminally.
The argument for removing members of Congress for not doing an investigation is even worse. The doctrine of legislative immunity is incredibly well-established, and the failure of a legislature to do something you think they should have done isn't actionable against them as individuals no matter what.
Apart from that, the whole premise of the argument is absurd. Congress has no constitutional obligation to investigate anything unless Congress determines it is necessary. Nothing in the Constitution gave the courts the power to make that determination. What the Constitution did do is leave it up to the states to choose their own electors. So if you want to go after how those states chose their electors, the proper remedy is to sue the states.
What is absurd is your statement.
...some lowly federal prosecutor bringing charges against a sitting President...
This is a private citizen bringing charges, not a federal prosecutor, lowly or otherwise.
...700 federal district courts around the country...
The Constitution grants Congress the power to enact laws.
Congress enacted 18 U.S. Code § 2381.
Note the first word...Whoever. No limitations.
The Court would merely be upholding laws passed by Congress itself.
It isn't my, nor the Court's fault, that Congress enacted their own demise.
Hoisted on their own petard.
US Code provides that the House shall investigate violations of oath of office and convict, possibly 5USC 7311 by House member(s).
The persons listed in the SCOTUS petition would then be barred from being part of the investigations.
Penalties for conviction are given in 18USC 1918.
If all in the petition were convicted, the House would be just 100+ members until state remedies applied.
With a new Speaker then selected, could just 100 House members impeach a POTUS & VP?