As LT said, I'd be most weirded out by the fact my T wouldn't know there's a new variant, given that it's all over the news. I think Ts should follow the news at least a bit, since they can often be very anxiety inducing.

I'd keep in mind that Ts are only humans. There have been times where - for a brief moment, a few minutes maybe - something was more about my T than about me. One time he had to have surgery, another time during the lockdown he had issues with his knees, I think there were one or two more such things. By about him I mean it wasn't that connected to my own situation, he wasn't sharing similar experiences or something like that, but purely "I have issue X".

He wasn't emotional during those moments though, and I can see why you'd have to say something about a surgery if you might be out for a week...
A fact to keep in mind that makes Covid a bit different is that this is very much a shared experience. Even if your T shares a trauma that you experienced, most of the time it wasn't the exact same thing. Maybe both of you were hit by your parents, but there are differences all over the place. That combined with the fact that usually Ts will have worked through at least part of their own issues when starting to practice, that means they can more easily distance themselves. However, if somebody pops up with new information about covid, that is a bit different, it will affect both of your lives directly, at this very moment. That can lead to some emotions. I don't think it's in general bad for a T to show those emotions, it can model how you can react to a situation. My T says sometimes that he's uncertain on how it's going to go, shares his opinions on people who don't get vaccinated (knowing my own opinion) and so on. I assume if I'd catch him with an important new fact that just came out, he might react a bit emotionally as well. So, I don't think you can completely compare this event to say her suddenly coming in and talking about her divorce for a whole session. It's probably more of a slip up, which will happen to every therapist from time to time.

The thing I'd certainly do is keep my eyes open for things like this happening again, especially if it's about other stuff. Other than that, my rule of thumb is always the same. If I'm still thinking about it when my next session comes around, I bring it up. And as for the how, I always say something along the lines of "you did or said X last session" and that it bothered me/wasn't the best thing to do/was out of line, whatever fits the situation best. If I'm not thinking about it anymore, it's a mistake that has happened, I can see past that. If it's a repeated thing, that'd be much different.

Edit: I'd also like to add that while therapy is mostly about you, sometimes a bit of small talk with questions back and forth are normal and okay as well. My T has asked me before about things about my dog (he doesn't have much experience with them) or about for example this forum. And those certainly weren't discussions where I took a whole lot from them, but for me it's not only a nice way to connect sometimes, but also to exchange information that I feel is important for my T. That's not the same as taking up the whole session or ranting of course, just a side note that in general asking a few things about a new variant you've never heard about would not be an issue for me in general.