moltenmetal....
I'm very sure, though "uninsured" may not be accurate in every case. It is certainly possible that other professional liability insurance policies don't prohibit professional moonlighting, at least in some disciplines.
Here in California, civil engineering (my and OP's profession) is a "Title Act" discipline, while chemical (your profession) is a "Practice Act" discipline. The legal standings of the two are quite different, as are the liability implications.
Years ago I was a principal in a small civil/surveying firm. Our professional liability insurance policy stipulated that moonlighting by professional civil engineers and surveyors in their licensed profession was prohibited, but I don't remember the exact language or all the implications. As I recall, if we knew about the moonlighting, our coverage was void; if we didn't know, it was still in force. Our policy was professional moonlighting results in termination. We didn't care about nonprofessional moonlighting. My current firm has the same policy.
The lawyers have made sure, at least in some cases, that a professional liability issue that occurs on a moonlight job can ping the employer's policy, whether or not the moonlighter has a separate policy. That why the insurers I am familiar with prohibit professional moonnlighting.
