Slowly more things become clear regarding the 2021 Minor League landscape. Here is an update on the matter.

Something that has struck my mind is that there won’t be any A Full Season circuit anymore, at least not for 2021. The two A Full Season leagues, the Midwest League and the South Atlantic League (or Sally League) will get another classification. The Midwest League will move up to High A, while the Sally League will be “demoted’ to Low A ball.
Besides that, the Florida State League will likely be decimated to ten teams, so two will be cut. What will happen to these teams is not clear yet. They may decease or they may become colllegiate teams.
Then, an overview of known affiliations for 2021 (and beyond?):
AAA
Those AAA teams that are (partially) owned by the parent club will remain at AAA:
Gwinnett Stripers (owned by Braves)
Memphis RedBirds (partially owned by Cardinals)
OKC Dodgers (partially owned by Los Angeles Dodgers)
San Antonio Missions (will move back to AA Texas League after spending 2019 at AAA)
SWB Yankees (partially owned by New York Yankees)
Syracuse Mets (owned by New York name sake)
Wichita WindSurge (moving to AA after not having played a single game at AAA)
The Rochester RedWings will part ways with the Twins, who will likely sign a deal with the St. Paul Saints.
The Fresno Grizzlies will become an A Short Season team in the California League.
The now independent Sugarland Skeeters are expected to affiliate with the Houston Astros. Not clear yet what will happen with the current affiliate Round Rock Express.
The Jacksonville Jumbo Shrimp will move up to AAA from AA and become a Marlins affiliate.
AA
Also in AA there are teams owned by the parent club:
Corpus Christi Hooks (owned by the Astros) (Texas League)
Mississipi Braves (owned by the Atlanta name sake) (Southern League)
Reading Fightin’ Phils (partially owned by the Philadelphia Phillies) (Eastern League)
Springfield Cardinals (owned by the St. Louis Cardinals) (Eastern League)
The Binghamton Mets will remain a farm team of the New York Mets for the time being. (Eastern League)
The Pensacola Blue Wahoos (Southern League) will likely join the Marlins farm system. With that, the club has its AAA and AA farm team in the state of Florida.
The Richmond Flying Squirrels (Eastern League) will remain a farm team of the San Francisco Giants.
As the New York Yankees move their AA (Eastern League) team to Somerset (Patriots), the Trenton Thunder is the odd team out. The team is offered a spot in the independent Atlantic League.
High A
The Carolina League will remain at the same level. The Midwest League will move up to High A as does the Northwest League. Note: High A was used for A-Advanced in the recent past but that name will disappear.
Also at High A level, there are MiLB teams owned by the parent club:
Carolina Mudcats (owned by the Milwaukee Brewers) (Carolina League)
Down East Wood Ducks (owned by the Texas Rangers) (Carolina League)
Winston Salem Dash (partially owned by the Chicago White Sox) (Carolina League)
Fayetteville Woodpeckers (owned by the Houston Astros) (Carolina League)
Salem Red Sox (owned by the Boston name sake) Carolina League)
Hudson Valley Renegades has joined the New York Yankees’ organization. The team will move up from Low A season to High A, likely in the new Mid-Atlantic League.
Dayton Dragons will remain a Cincinnati Reds affiliate. (Midwest League)
The Cedar Rapids Kernels will remain with the Twins. (Midwest League)
The South Bend Cubs will remain with the Chicago name sake. (Midwest League)
West Michigan WhiteCaps will remain with the Detroit Tigers. (Midwest League)
Boise Hawks will remain with the Colorado Rockies. (Northwest League)
The Brooklyn Cyclones will remain a Mets affiliate, likely in the new Mid-Atlantic League.
Everet AquaSox remains with the Mariners (Northwest League)
Low A
The Sally League, the Florida State League and the California League will all move down a (few) level(s).
Note: Just like A-Advanced, the term A Short Season will disappear and will be replaced by Low A. What used to be Short Season will be eliminated. So in fact only A-Advanced (named High A) and A Full Season (named Low A) will remain.
Just like the other leagues, some Low A Season teams are owned by the patent clubs as well:
Hickory Crawdads (owned by the Texas Rangers) (South Atlantic League)
Rome Braves (owned by the Atlanta parent club) (South Atlantic League)
Bradenton Marauders (owned by Pittsburgh Pirates) (Florida State League)
Clearwater Threshers (owned by the Philadelphia Phillies) (Florida State League)
Jupiter Hammerheads (owned by Miami Marlins) (Florida State League)
Lakeland Flying Tigers (owned by Detroit Tigers) (Florida State League)
Modesto Nuts (Mariners are majority owner) (California League)
Palm Beach Cardinals (owned by St. Louis parent club) (Florida State League)
St. Lucie Mets (owned by New York parent club) (Florida State League)
Tampa Yankees (owned by New York name sake) (Florida State League)
Dunedin Blue Jays (owned by the Toronto Blue Jays) (Florida State League)
San José Giants (owned by the San Francisco name sake) (California League)
The Fresno Grizzlies will move to the California League. So far the team doesn’t have a parent club.
The Florida FireFrogs have left Kissimmee for North Port but are a potential candidate to be eliminated by MLB.
For now the fate of the New York-Penn League is unclear as is the fate of the Pioneer League.