If your job doesn't allow you time to learn tools that can be used in your job, that's a definite problem.
That said, like others have already said, the task of keeping up with the JS ecosystem is futile. Yeah, there might be some cool new tools, like esbuid, Vite, and Nuxt, but that doesn't mean you have to always jump on those bandwagons.
A real non-problem with ecma/javascript language is that it is almost too easy to start writing that there is always someone putting some new tool out for it. This means there is always competition with similar tools, people trying to shout about how their shiny tool X fixes problem Y better than other tool Z. It's easy to get caught up in the noise.
Here's my hot take: don't try and keep up on your own effort. Use tools that you understand and are time-tested. Sometimes, a co-worker might be using some new shiny tool, and when they do, ask them to show it to you. It doesn't mean you need to switch to it, but it gives you an opportunity to learn the top level overview/benefits without having to keep track of everything.
A big thing I try to do is avoid following JS libraries/personalities on places like twitter. Every day, they are touting their own tools and tooting their own horns - there is nothing wrong with that, but it's just noisy.
And let me say this, no one will get fired if the tools you use do the job they need to do in a easy and consistent way.