was never divided into "Division 1" and "Division 1A." In 1971, the schools decided to create the 3 division levels within the NCAA organization. In 1978, the Division I schools decided to create 2 subdivisions for football; DI-A and DI-AA. In the early 2000s the DI schools decided to rebrand the 2 subdivisions into DI-FBS (formerly DI-A) and DI-FCS (formerly DI-AA) because the schools felt people perceived the DI-FCS was not considered DI football even though the NCAA considers the DI-FCS champion to be the NCAA DI Champion in football. Those 2 DI subdivisions still exist today.

Now when the DI-FBS schools decided to create the Bowl Championship Alliance (BCA), the private organization included all the existing DI-FBS conferences except for the Big Ten and Pac-10. Those 2 conferences and Rose Bowl chose to not participate because they wanted to preserve tradition. Eventually the Big Ten, Pac-10, and Rose Bowl reconsidered its position. As a result, the BCA was rebranded into the Bowl Championship Series (BCS). The same private organization that ran the BCA ran the BCS with the addition of the Big Ten and Pac-10. As a result of public outcry, the schools decided to rebrand the BCS into the College Football Playoffs. The private organization that ran the BCS currently runs the College Football Playoffs.

In order for there to be a 4-team playoffs, the NCAA DI bylaws did have to be changed. However, it was more or less just a rubber stamp because the BCS Presidential Oversight Committee members wouldn't have voted to submit the proposal to the NCAA Board of Directors unless it already had their support. You can find the exact chronology of how the College Football Playoffs came about, how the terms "P5" and "G5" came about, and other relevant information on the College Football Playoffs' website. It is worth noting that the terms "P5" and "G5" came about during the November 12, 2012 meeting in Denver.

"Monday, however, the commissioners and presidents who oversee the sport agreed to include a guaranteed spot in one of the six premier bowls for the highest-ranked champion (as determined by the new selection committee) from the so-called "Group of Five:" the Big East, Conference USA, MAC, Mountain West and Sun Belt."

https://www.si.com/college/2012/11/13/college-football-playoff-six-bowls

The NCAA, regardless whether you are referring to the administrative body or its members (aka schools), weren't really involved in the decision. It was the schools, who happen to be NCAA members, that were involved with the BCS who came up with the terminology to avoid potential antitrust lawsuits. The NCAA, via its various committees which are basically made up of representatives from the various DI schools, rubber stamped the proposed change in the bylaws so the College Football Playoffs could move forward.

The reason the expiration date of the current contract matters is because the College Football Playoffs LLC (aka the private organization the runs the daily operations) is tasked with negotiating the new contract. If you look at the governance of the College Football Playoffs LLC, then you will see it is the 10 FBS conference like I stated earlier.

https://collegefootballplayoff.com/sports/2019/4/3/governance.aspx

Likewise, the College Football Playoff LLC is also responsible for proposing any changes to the NCAA DI bylaws. Since the various NCAA committees will basically rubber stamp any proposals submitted by the College Football Playoff LLC, the LLC is ultimately the one who decides how many "Ps" and "Gs" exist within the FBS. For the next contract it could remain P5 and G5 or it could change to some other combination depending on how many FBS conferences exist. FWIW if you look in the 2020-21 NCAA DI Manual, then you will find no mention of "P5" and "G5" in it. Heck you won't even find the requirement that the highest ranked G5 champion receives an automatic bid to a NYD6 bowl game because that is a College Football Playoffs rule.

https://www.ncaapublications.com/productdownloads/D121.pdf