The June 2021 press release on the status - an excerpt:

The working group was appointed by their management committee colleagues and has met over a two-year period to discuss possible new formats. The proposal calls for the bracket each year to include the six highest-ranked conference champions, plus the six highest-ranked other teams as determined by the College Football Playoff selection committee. No conference would qualify automatically and there would be no limit on the number of participants from a conference.

The four highest-ranked conference champions would be seeded one through four and each would receive a first-round bye, while teams seeded five through 12 would play each other in the first round on the home field of the higher-ranked team. (The team ranked #5 would host #12; team #6 would meet team #11; team #7 would play team #10; and team #8 would meet #9.) Under the proposal, the quarterfinals and semifinals would be played in bowl games. The championship game would continue to be at a neutral site, as under the current format.

Reading this as written.

This would mean that the top six conference ranked champions would be seeded 1 through 6 with 1 through 4 getting byes. Five and six would not. No conference is designated as a top six, just that the top 6 ranked conference champions of the 5 P5 and 5 G5 conferences would be seeded. Seems odd to me, but whatever.

Teams 7 through 12 are chosen based only on rank at the time of seeding. This is where the SEC would do well, with the Big Ten probably right behind them. Notre Dame would fall into this competitive group fighting for a seed.

Assume:
#1 - SEC Champion - Alabama
#2 - Big-12 Champion - Oklahoma
#3 - Big Ten Champion - Ohio State
#4 - ACC Champion - Clemson
#5 - Pac-12 Champion - USC
#6 - AAC Champion - Cincinnati

#7 - Notre Dame
#8 - Georgia
#9 - Wisconsin
#10 - Oregon
#11 - Florida
#12 - LSU

The SEC would place 4 teams, the Big Ten and Pac-12, just 2 and the Big-12, ACC and AAC just 1 each. Notre Dame would be the lone independent.

1 - 4 get byes
5 vs 12 - LSU @ USC
6 vs 11 - Florida @ Cincinnati
7 vs 10 - Oregon @ Notre Dame
8 vs 9 - Wisconsin @ Georgia

It would not be a tough step to designate conferences and the limit of no more than two from any conference.

If that happened in this case, Florida and LSU would likely be eliminated and replaced with a second ACC and Big-12 team - possibly a G5 or BYU if still independent.