In the January 2023 crisis over electing Speaker of the House in the U.S., usually one of the first things mentioned in any coverage is that without a Speaker, "House members can't even be sworn in". E.g., at ABC News:
The House can conduct no other business -- and members can't be sworn in -- until a speaker is chosen.
However, almost all of the House members, including newly-elected members, appear to be present, seated, and voting in the current Speaker election cycle. E.g., each of the first seven rounds of voting for Speaker in 2023 had 434 votes cast (including "present" votes, per NY Times), which is only one less than the full Congressional membership (Wikipedia).
This SE Politics Q&A seems to give competing clues on the issue. The question asserts that the Clerk "convenes" the new Congress on Jan-3. The selected answer seems to support this, citing House rules that say the Clerk "shall call the Members... to order". But the second answer cites a SCOTUS case in which the creation of a Congress and its processes are dependent on members having "taken the oath, been sworn, and entered upon the rolls".
The U.S. Constitution (Article I) seems to have little to nothing on the details of these procedures, the only nearly-relevant parts being (Sections 2 and 4):
The House of Representatives shall chuse their Speaker and other Officers; and shall have the sole Power of Impeachment... The Congress shall assemble at least once in every Year, and such Meeting shall be on the first Monday in December, unless they shall by Law appoint a different Day.
And from Article VI:
The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States.
So: What exactly can elected members of Congress do prior to being "sworn in" -- and what is different that they can only do after being "sworn in"? (Also, secondarily: What is the criteria for the first part, i.e., exactly what triggers members of the House to be active-but-not-sworn-in, and when does that occur?) Citations to the Constitution, law, or official House procedure documents for a best selected answer.