This is a complicated question.
Up until a little while ago, I was an appointed moderator on the network. I... spent a lot of time in the TL; I was among the chattiest users in the room the couple times a CM pulled out stats on it.
Most of the time, the TL was just like any other room - it had its "core members" who would often be around and chatting. There were often ~60 people constantly lurking in the room, and I estimate around ~25 people who would be pretty reliably around in the room - notably, these were often the moderators who spent a lot of time on chat in general. It's worth noting that the vast majority of moderators do not use the chat system at all, or very rarely. There was a large percentage of moderators who would pop in now and then, either to ask a question or just to chat, but didn't have a regular presence in the room.
Unlike most rooms, the TL also serves as a way for moderators to contact a CM or the mods of another site, with an internal bot that helps with this. This would mean that moderators who want to grab a CM would often have to jump into the TL to ask their question... which meant that the people who hang out in the chat room would see the question as well.
Often, that would result in someone poking their head in to ask a CM something, and then unexpectedly getting half a dozen of their peers giving them an un-requested answer instead.
This can probably be chalked up to a genuine desire to help - most of the people answering genuinely wanted to help out - but it would give the impression of being jumped on if you weren't expecting it. If I ask Shog a question, I'm not expecting an answer from seven moderators coming at me all at once. You can feel ganged up on.
This was especially pertinent in cases where perhaps you disagreed with a certain policy or your site handled certain cases in a different way. You suddenly had sometimes up to a dozen people at once questioning you, complete with the loud, annoying chat ping sound, and telling you you're doing it wrong.
That's definitely toxic. Even though it was all good-intentioned, you still feel like you're under attack. That's not why you came into the room - you came to ping a staff member and suddenly you're being attacked by a dozen people you don't know.
At times, in the TL, there were long drawn-out discussions (emphasis on that word) about difficult topics. I distinctly remember having discussions about gun control, homeschooling, and cigarette smoking in the TL, with people who I strongly disagreed with... and it didn't devolve. The discussions remained mutually respectful, with people actually talking and responding to each other's points with real arguments. There were attempts to understand the other's point of view. It was an exemplary case of productive discussion of a charged topic.
These discussions would go on for hours at times, and most of the time the conversation would end well (or just straight-up dissolve into a pun war).
But sometimes... there were the arguments.
These arguments were, at a glance, very similar to the aforementioned discussions. They would involve people discussing a topic for hours... but with crucial differences.
These arguments were sometimes about the very same topics that had previously had productive discussions. Often, they were sparked by somebody coming in who hadn't been around for the discussion, who might've read the transcript or seen something on the starboard, and decided to respond. These arguments weren't so calm. People would get frustrated at each other, and remain entrenched in their positions. Nobody was willing to see the other side.
That's when problems developed.
Since it's the TL and everybody is a moderator, there is no way to force a conversation to end. With a normal user, a moderator or Room Owner can kick them out of a room in an escalating 1 - 5 - 30 minutes, preventing them from talking in that room during that time. A moderator can issue a suspension ranging from an hour to 9999 hours. A room owner can put a room in timeout, or a moderator can freeze the room. There are a lot of methods to stop a problematic conversation that won't end.
But a moderator is exempt from all these things. They can't be kicked or suspended. They can talk, even if the room is in timeout or frozen (or, heck, deleted). There is no way to stop a problematic conversation in the TL.
And that caused problems. Since there was no way to force a conversation to stop, the arguments would continue, sometimes dragging on for days, until people got sick and tired and disgusted and just left. It would slowly poison the room until it was finally over. People would leave with a grudge against some other moderator, that they would nurse and only make worse. And there was no way to stop these.
Luckily, these arguments were infrequent... until recently.
As soon as the messages that started this current debacle were dropped into the TL, the TL exploded. People who hadn't ever really been involved in the TL much suddenly became really active there, and there were more people talking than ever before. And they were all talking about one thing... or, well, several things, but they were all related.
There wasn't a break in the transcript for the length of an hour until several weeks in.
And in those several weeks, the TL I knew changed. The people I had enjoyed productive conversations with, had pun battles with, and considered my friends... most of them I couldn't find in the mess. The TL was filled with different people.... arguing. For weeks on end.
And suddenly, there were no more discussions. It was all arguments. And those arguments that I was dismayed to see in the first place, then came to include anti-queer comments. And anti-Jewish comments. People were tearing each other to pieces, painting targets on people who weren't there, painting targets on people who were there...
Most people weren't interested in listening. They wanted to talk... and they did. They talked and talked and talked, and even when they said something offensive, there was no way to point that out or remove it without getting swallowed alive by the argumentative crowd that now filled the TL.
Everyone was bitter and angry and it turned the TL from a level-headed place into a room boiling over with frustration and grudges. It got nasty.
I was suddenly seeing messages about not wanting to respect people's pronouns accrue a dozen stars in the space of ten minutes. I saw vitriolic messages spouted about my religion. It became an extremely toxic environment.
...this all contributed to my feeling unsafe remaining a moderator, and was a large factor in my decision to resign.
To address the original question, though: Is the TL toxic?
It both is and it isn't, I'd say. It definitely has toxic qualities - for instance, the common piling on that happens to hapless people just asking a question - but the room when it is operating normally isn't toxic.
But it has the capacity to get very toxic very quickly, because there is no way for the moderators to moderate the moderators. Because there is no way to moderate the room, it at times becomes extremely toxic and has a hard time getting out of that once it falls in.