The Hubble Tension is certainly real. The Hubble Constant can be estimated from a number of completely independent astrophysical phenomena. There is a significant difference in the value computed from 'local' phenomena, and distant phenomena. It is often referred to as the "5 sigma" tension, because that is the statistical significance of the disagreement. This has been know long before James Webb, but as the article says, these observations just lowered the uncertainty on one of the probes. But we were fairly certain already that this tension is real.

Whether it's a crisis or not is up to the individual. Things not agreeing in science

especially astrophysics/cosmology

is just part of the process. I don't know anyone that is 'worried', so much as looking for ways to solve the problem.