Doom85
Member
I mainly mean the animated movies that came out post-2014/2015 up until recently, where WB were just kind of releasing a string of animated movies where the characters shared the same exact designs throughout each, but they were disconnected stories. The Batman in each one looked the same, which was this design:
They weren't disconnected, in fact they were all part of the same universe: the DCAMU (never officially named, but this became the fan consensus for its name). All the prior movies were stand alone (aside from the two Superman/Batman films which were implied to be connected), often direct adaptation of specific comic runs or miniseries. But the animated film Justice League: The Flashpoint Paradox's ending saw the start of a new universe which got fully started with Justice League: War and continues from there, with most animated films from then on being in that universe.
That universe ends with Justice League Dark: Apokolips War, which ends with the start of a new universe. This new universe never got an official name either but fans dubbed it the Tomorrowverse as the animated film Superman: Man of Tomorrow was its first entry. The Tomorrowverse for ten films altogether, ending with the three-part film Crisis on Infinite Earths.
You can read more about it, and see the full list of films here:

DC Animated Movie Universe
The DC Animated Movie Universe, or DCAMU, is a Shared Universe based on The DCU that exists as part of the DC Universe Animated Original Movies line, starting in 2013 with Justice League: The Flashpoint Paradox. All movies in the line, which …

I've not started the Tomorrowverse yet, but I've heardly roughly only the first half of its films are worth watching, with the Justice Society film being its best one. The DC Animated Movie Universe though is mostly good even if I feel a lot of the stand-alone films before it were better. But, I recommend stopping before Apokolips War, watch if you're a completionist, but for me, it was just a ridiculous over-edgy (to the point it felt like a parody at times it went so far) murder fest of the heroes that feels completely unsatisfactory as the conclusion of their universe.
Also, for the Tomorrowverse, if you haven't read Batman: The Long Halloween, I highly recommend doing so before watching the animated film. The animated film is mostly a decent enough adaptation from what I remember, but it absolutely butchers the ending which pisses me off as the comic's final few pages is IMHO a legitimate great plot twist that I did not see coming. The movie has that plot twist….and then keeps going past it and everything they added was unnecessary and awful to me. As it is my favorite Batman comic and my third favorite DC comic series overall (after DC: New Frontier and All Star Superman), I did not take kindly to that.