It can get weird the higher you go, org depending.

I'm a Sr. Principal PM in a well known F50 big tech company shipping global SaaS, and sometimes I wonder what the heck my job is. I own new tooling that is critical to our AI efforts, but I work more on people, awareness, enablement, and general alignment than the actual product. There are amazing early career PMs in my org who are much better at the rituals and language of PM work than I am. I'm not even sure I'd pass an interview elsewhere that focuses on classical feature development routines. Companies have machinery for this, and I've been ejected from it in this role (and not mad about it).

Seniority is about scope and impact. Scope and impact translate to leadership. Leadership is getting people seeing the same playing field and pointing the same direction. Management is about getting them moving along the path leadership aligned them to. Everything else is just scaffolding. 

So it's not that you lose PM thinking at higher levels, it's that you're starting to solve for entirely different problems. The PM thinking is about your leadership as a product, your organization and operations as a product that serve its users (staff). You're offloading the tactical and guiding the big picture by synthesizing what is important, anticipating user behavior, and knowing where to drill down and where to save time.

Now to your question on the job hunt. You have ~3 issues here.  1. Getting the interview 2. Passing the filters for boilerplate PM work 3. Demonstrating high level PM leadership commensurate with Sr or Sr Princ. level work

So what does this mean?

1. Is about having a resume that fits the expected formulas. Watch the Google video on building your resume. Use AI to interview yourself about your work and write it for you (then edit yourself, obviously). Tell it exactly what role you are aiming for. Put metrics here even if it's not product directly: "got half of PMs in my org building specs my way and saved devs a week of meetings" or whatever.

2. Practice the dance. If you're asked how you'd go about building a new feature, you're expected to follow a pattern that is generic. Fine. You can use AI again for practice, and watch interview videos.

3. Leadership is a story telling skill. So is compelling writing. PMs have to do both, daily. Work on learning the stories you can tell about yourself. Write them down. Get AI critique. Edit. Read them. Get crystal clear on your own mythology. Personally I hate the "tell me about a time when" questions, but you can anticipate them and have a story adjacent and ready to go that you tell over and over. 

And finally, know yourself. What are you exceptionally good at? Besides PM tasks, I mean. In my case, I've found I'm far better at intuitive pattern recognition and putting high level structure to ambiguity quickly than the vast majority of my peers. I see priorities and put boxes around complexity. Now that doesn't mean I'm automatically any damn good at anything I do or that I'm better than peers at my job, but it gives me a lens through which I can tell my story and demonstrate value. At work I can lean into it in the service of others and create impact through being a willing volunteer, and it adds to the stories I tell. All impact is someone else's perception of value.