I mean the LWR fleet has proven to be incredibly safe by any objective measure with deaths per TWhr as good or better than wind/solar. The very incident you mentioned had a direct death count of 0 or 1 depending on who you ask. Industrial shit blows up all the time, you just don't hear about it because it's normal and accepted.
What needs to improve about nuclear is our ability to deliver it on time and on budget. Safety is already more than adequate.
That is never going to happen until we are building more of a consistent design. I think every LWR is use today is a custom bespoke piece of equipment.
Yes, standardizing on a handful of designs will help immensely, as well as building two or more reactors on one site to share the overhead costs between units.
For example, building out more AP-1000s is really a no brainer. The first-of-a-kind is always expensive and the AP-1000 was especially so due to many factors. We bore that cost and now we should reap the benefits of Nth of a kind builds.
What needs to improve about nuclear is our ability to deliver it on time and on budget. Safety is already more than adequate.