There's a difference between no demand, and none realising they need your services.
Can't hurt to ask, or even put yourself out there 🤷🏻♂️
Discussion
If that's the case, then the question becomes, "Is my new employer willing to admit that they don't know what they're doing?". A company that makes software, (especially critical software) and doesn't know they need QA, is clueless about the industry they've entered. Places like that need a new CEO before they need anything else.