Just my perspective so take it with a grain of salt. It helps to look for positions outside the normal SV roles so places like aerospace, defense contractors, manufacturing, etc. They post a surprising number of CS positions. I would caution, though, that the only role I've seen that pays SV-type salaries ($250k+) was controls engineer for automotive manufacturing. But to be fair, the jobs were all in areas with a cost of living much, much lower than SV.

If you get in (politely) look for processes that your SE skills can make an impact. These opportunities are sometimes there because the place is full of non-software minded folks who don't know what they don't know. An example from my anecdotal experience was when someone with software acumen helped reprogram an automation system to be more efficient and saved high-six/low-seven figures each year and really gets people's attention. Or showing how they can dramatically improve their quality control by developing unit tests. Some stuff that is common in SE firms is often overlooked in firms focused on other disciplines.

The most common paths for people making mid-career moves to finance are from using software skills in industries like aerospace, defense contractors or manufacturing?

That doesn't sound right. I'm not even sure most people transitioning into finance from another career have any software skills at all (beyond Excel).

Sorry, I lost track of the thread comments. I thought the question was how to move from SE to hard engineering fields like mechanical or civil.