Ok so regarding The Batman being a prequel to Teen Titans, I think there is absolutely enough evidence that this can be the case without any contradiction. This theory has been picking up speed in recent years and I'm all for it. Aside from Robin being the most obvious evidence for this, I think many people overlook the connection between Rumor and Slade. Let's break it down.
Mario is the anti-heroic antagonist of The Batman episode "Rumors". He was formerly Paul Karon's bodyguard, but after failing to protect him, he became the vigilante named "Rumor". Originally Hush was intended to be the villain, but DC did not like the idea, and created Rumor in his place. Unlike Batman he has no code of ethics as he told the villains that killing them is something Batman does not have the guts to do. He even tells Batman that he should have become more brutal as a vigilante.
Now, if one looks at Mario/Rumor and compares himself to Slade from Teen Titans, there are A LOT of similarities that could make one believe they are supposed to be the same person. I like this idea so much and it works really well. Let's see what Rumor and Slade share in common. First of all, they are both muscular males that have brown eyes. In the Teen Titans episode "Forces Of Nature" we get a glimpse of Slade's brown eyes, which match Mario's.
Earlier in the season we do see Slade in what appears to be blue eyes, but this is the only case I've noticed this. All subsequent appearances he has black/brown eyes. Maybe he was wearing a blue contact that day?
We know Slade is Caucasian from the episode "Betrayal" where he took some damage to his suit, revealing his skin tone. This tone matches Mario's.
Mario seems to have light brown/red hair. We never get a good shot of Slade's hair until "Apprentice, Part 2". Seeing that it's in shadow, a case could be made they both have brown hair.
In the Teen Titans episode "Haunted" when Raven is in Robin's mind, there is a glimpse of Robin swearing an oath to Batman. This is Batman's only appearance in the series.
A second flashback shows Robin's parents, John and Mary Grayson, falling to their deaths; due to a sabotaged trapeze wire during a circus performance, which The Batman portrayed in "A Matter Of Family".
"Haunted" has the strongest evidence of Slade's true identity being that of "Mario" from "The Batman" episode "Rumors". The following exchange shows this.
Robin:
"Why couldn't Starfire see you?"
Slade:
"I believe you are familiar with cloaking technology?"
Robin:
"I'm familiar with all your tricks."
During the episode "Rumors", Mario used cloaking technology when utilizing his Rumor identity to battle Batman and Robin. This is how Robin would be already familiar with cloaking technology, which we never saw utilized before "Haunted". This means Slade is referring to a previous time he encountered Robin before the series. The episode "Rumors" showcases this.
Also, considering in that episode, Rumor was able to singlehandedly capture nearly all of the major Gotham City villains - something Batman himself couldn't do - it's very likely that there's more to Mario than he let on. In fact, Mario may not even be his real name. Slade is the identity he chose sometime after the events of "Rumors" and he's been after Robin ever since. Robin doesn't even know the true identity of Slade, which further adds to the mystery surrounding the character.
Both Slade and Rumor possess Enhanced Physical Capabilities, Genius-level Intellect, Vast resources (power suits, weapons, tech, etc.) and are both Master combatants. Both are experts with the Bo Staff as well. Their similarities don't end there, they are also both voiced by Ron Perlman, which just further cements the idea that these are supposed to be the same person.
