I had similar concerns before I joined up. I didn’t want to get swallowed up in some massive project or shuffled around in reorganization after reorganization.
The guy who was recruiting me made all the assurances that would not happen. I respected this guy, it’s the only reason why I even entertained being “recruited” for this role. Even with that though his word was not good enough.
What put me over the edge was meeting with his boss and then his bosses boss. I got the impression that these people had great skills in running an organization. They both were ex engineers who made the leap to senior management prior to joint the mega Corp (VP and Exec VP). I felt like I could trust them to a degree. It has proven out for me.
So, I suggest trying to get information to gauge how much you can “trust” your senior leadership beyond whomever will be your supervisor since those are the people who will really have the most control over your agency and future at that company.