And transfer all the pressure to your project's VCS maintainer, who is also being told by management to use AI?

At some point you need to start thinking whether the product your company wants you to make is really worth it.
You might not think about it right now, but you might, by the time your company starts paying you in AI token allocation.

What kind of web app is your company making that it somehow requires you to learn and use all the new frameworks?
And if you are having to learn the framework despite your product not requiring it, perhaps the priorities of your seniors are misguided or you are trying to fulfil the wrong JD (R&D perhaps? I would love such a job, but I won't be choosing JS either way).
It is the job of the management the place the correct person onto the correct position and if they are making you do something that is killing you, perhaps they need to be replaced. And if you always only cared about [paying the bills, well there will soon be more bills to pay, the way we are going.

I only had to use some plain JS for my website (not a web app though) and I recently had the opportunity to remove even that.

I am always happy learning new libraries and frameworks and technical concepts even if I only end up using them just in a single project. I am learning Lua just to be able to make an extension of a game I am not sure I will be playing 5 years down the line.

But I also rid myself of everything uninteresting. I forget the names of programming concepts, design patterns and language features that I am using regularly (sometimes to my own detriment), while associating the patterns to functional requirements in my mind.

When I feel cognitive load rising, I don't think of making the task simpler, but increasing my concentration, because that's what makes the work desirable to me. And there will always be something that will require you to load your brain as long as you want to create something with emphasis to quality.
Previously made processes will require reimagining the reasons behind their making and deconstructing them to create better processes. Undocumented code will have to be checked and the intent behind it be understood before checking to make sure that AI generated documentation represents the correct design. Even C++ developers moving to Rust will find out that there are more things that are not yet explicit enough and require reading and correlating to other functions in the codebase.