Earlier quoted context omitted.
Would be interesting to compare this across areas. My impression is that eg Finance (another popular destination for mid-career switches) is far more open in that regard. Experience, even if it's in a different field (as long as it's a technical role or one that will give you a rich set of contacts) seems to generally confer seniority. Would be interesting if someone could weigh in.
What are some common paths for people who make that jump?
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.