It’s still the accepted theory among the majority of astronomers & physicists. Some of the big questions that remain are dark energy and dark matter

Right! It’s actually not that the Big Bang theory is the problem itself - it’s the best framework we have so far that makes sense of all the observations (e.g. the expanding universe, the cosmic microwave background radiation, etc). The features that you’re referring to are dark energy and dark matter. We still don’t understand what those really are, and if we want to understand our entire universe and its expansion we need to get a handle on those two. And that’s where JWST will hopefully come in. I’m excited to see what we find out!

The JWST results so far have not contradicted the Big Bang Theory. That article is contributing to misinformation and fear mongering, tbh. As Dr. Becky’s video (that u/wanderlustcub shared) explains, cosmologists are actually excited to see if JWST proposals will help constrain the “crisis in cosmology” which is basically the Hubble constant, or rate of expansion of the universe.