Adding to the analysis of Rule XXII. The mention of Rule IV is pretty obvious.
Whenever the Senate is proceeding under paragraph 2 of rule XXII, the reading of the Journal shall be dispensed with and shall be considered approved to date.
As for the mention of Rule II, look at XXII(2)
Notwithstanding the provisions of rule II or rule IV or any other rule of the Senate, at any time a motion signed by sixteen Senators, to bring to a close the debate upon any measure, motion, other matter pending before the Senate, or the unfinished business, is presented to the Senate, the Presiding Officer, or clerk at the direction of the Presiding Officer, shall at once state the motion to the Senate, and one hour after the Senate meets on the following calendar day but one, he shall lay the motion before the Senate …
Parliamentary Law says that a motion on the floor has precedence until disposed of. So what happens if a new Senator presents their credentials during the lag between the cloture motion being stated by the PotS and the action taken on it?
Rule II(1) states
The presentation of the credentials of Senators elect or of Senators designate and other questions of privilege shall always be in order, except during the reading and correction of the Journal, while a question of order or a motion to adjourn is pending, or while the Senate is voting or ascertaining the presence of a quorum; and all questions and motions arising or made upon the presentation of such credentials shall be proceeded with until disposed of.
So the mention of Rule II affirms that the presentation of credentials is always in order if Rule XXII is in effect.