As far as I can see, the exact text of the amendment to the RNC rules hasn't been published yet - at time of writing the Rules & Resolutions page on the GOP website has only been updated to include those made at the 2021 Summer Meeting, while this resolution was recommended to the Rules Committee at the 2022 Winter Meeting, and adopted at the 2022 Spring Meeting. Speaking at the Winter Meeting (at 46:00), Dave Bossie, who chairs the Committee on Presidential Debates, told delegates that a copy of the amendment could be found in their conference materials, but it doesn't look like these have been made available to the public at large.
Nevertheless, various excerpts have been released, so we can draw some conclusions from these. In fact, the provision is very similar to one that was in effect during the 2016 presidential election.
The most complete text I've been able to find was carried by CBS News:
"All presidential primary candidates shall also agree in writing to
appear in only sanctioned Primary and General Election debates," the
amendment said. "Any presidential primary candidate who does not agree
in writing or who participates in any debate that is not a Sanctioned
Debate shall not be eligible to participate in any further Sanctioned
Debates."
The amendment includes language about a temporary committee on
presidential debates that would approve and sanction debates for the
RNC.
What does the statement each Republican presidential candidate must sign say exactly?
The amendment doesn't appear to proscribe any particular language for the statement, it just seems to be an agreement to only appear in Primary and General Election debates which have been sanctioned (as in approved) by the temporary committee on presidential debates.
What (if anything) can the RNC do to force every Republican presidential candidate to sign?
Not a massive amount really - the penalty for not signing is set out in the quotation above; they will not be eligible to participate in any further sanctioned debates. However, the Republican Party only really has the power to block candidates from primary debates that it sponsors itself; the candidate would be free to participate in any other debates during the primary, and if the candidate was successful in the primary, the Party would have no power to prevent them participating in the General Election debates.
What if a candidate signs but then breaks the agreement in some way, what (if any) penalties can the RNC threaten to keep its candidates from debating on non committee-sanctioned platforms?
Similar to the above answer - not an awful lot. The only penalty detailed in the rules amendment is the loss of eligibility to participate in further sanctioned debates.
What exactly constitutes an actual debate according to the statement the RNC requires?
Those debates chosen by the temporary committee on presidential debates. The WSJ carries more details on this body:
The RNC plans to form a working group to sanction debates based on input from presidential campaigns and criteria that may include timing, frequency, format, media outlet, candidate qualifications and the “best interest of the Republican Party.”
This seems awfully similar to a provision which was implemented in 2014, but was removed at the Spring Meeting in 2018 - from the 2016 Rules:
The Standing Committee on Presidential Primary Debates shall have the authority to sanction debates on behalf of the Republican National Committee based on input from presidential campaigns and criteria which may include but are not limited to considerations of timing, frequency, format, media outlet, and the best interests of the Republican Party. Each debate sanctioned by the Standing Committee on Presidential Primary Debates shall be known as a "Sanctioned Debate." Any presidential candidate who participates in any debate that is not a Sanctioned Debate shall not be eligible to participate in any further Sanctioned Debates.
In 2016, however, a written statement from each candidate was not required, and there was no reference to 'candidate qualifications' as the WSJ suggests is present in the new rule.
