Despite Batman warning Amanda Waller he'd "shut down" Task Force X if she didn't, the Dark Knight is nowhere to be seen during the events of 2021's Harley Quinn, and the concept of the Suicide Squad itself - it does clearly continue on in the same timeline, as is evidenced by Boomerang asking Harley how she'd ended up back in the team of government-controlled villains.
As such, the question naturally emerges as to how exactly the group is still operational, given that Suicide Squad closes with Bruce Wayne confronting Amanda Waller about needing to shut down the program, despite the fact the latter revealed an awareness of his secret identity. There is clearly some time between the first and second film, which makes this matter even more confusing, as it makes it even more blatant that Waller has entirely disregarded Batman's warnings, and yet the matter isn't really addressed in the movie.
This real-life explanation for this is of course that Amanda Waller gathering a series of superpowered misfits into one ragtag team is certainly concerning, but it pales in comparison to many of the other threats occurring in the universe around this point in time, and thus it does make sense in-universe why Batman doesn't follow up on his threat.
In fact, this may also serve to explain why The Suicide Squad is comprised of far less powerful figures - or at least, individuals that don't seem as blatantly powerful as the original cast. While Suicide Squad had a mystical otherwordly supernatural entity in the form of Enchantress, and a man capable of burning town a town within a matter of minutes through Diablo, the updated team is far less imposing. This places even less precedent on dealing with the Squad for the Dark Knight, meaning Waller may have intentionally selected a group of more eccentric individuals in order to avoid having to deal with Batman. However, she did also pick Bloodsport, who is famous for having shot Superman with a Kryptonite bullet, so she may have also been laying the foundations for a team capable of dealing with Batman's allies if it came to it.
This all said, The Suicide Squad arguably benefits from the absence of Batman in the film, as the focus on the largely obscure comic characters that are used would have potentially been undermined by his appearance. Though the movie does continue the personal plots of both Waller and Harley Quinn, its highlight is the way in which it utilizes characters that would have otherwise never been used in a big-budget film, legitimizing the likes of Suicide Squad 3.
