I'm not sure if they are basing this on any version of the team in the comics. I'm only familiar with the original version of the Thunderbolts from the 1990s.
The original concept of the Thunderbolts was that they were a new hero team who showed up while the Avengers were missing in action. They presented themselves as an all-new set of heroes stepping up to fill the gap left by the missing Avengers. Secretly, however, they were all villains recruited by Baron Zemo, posing as heroes to gain the public's trust.
This version of Thunderbolts appears to be made up of characters who were already in the MCU as heroes, antiheroes, and villans:
- Black Widow II - Yelena Belova (Florence Pugh)
- Taskmaster - Antonia Dreykov (Olga Kurylenko)
- Winter Soldier - Bucky Barnes (Sebastian Stan)
- Red Guardian - Alexei Shostakov (David Harbour)
- Ghost - Ava Starr (Hannah John-Kamen)
- U.S. Agent - John Walker (Wyatt Russel)
- La Contessa - Valentina Allegra de la Fontaine (Julia Louis-Dreyfuss)
It seems like they are going for more of a straight-up Dirty Dozen/Suicide Squad approach for this movie.