Update questions for the request to publish and for the form publishing to allow data collection for archetypes

Recent CX and GC Forms sync discussions highlighted two connected needs:
- Improve how the product collects data about user archetypes;
- Have a more structured understanding on how much the work clients do with GC Forms aligns with broader government priorities.
At the same time, the product team is reviewing the sign‑in experience, creating an opportunity to revisit the questions asked at two key points in the product journey:
- Request to publish
- Pre‑publish check
Additionally, previous UX research for GC Forms used a series of questions during the recruitment screener, with the intention to identify participants who fit the scope of that study and reflected areas connected to government priorities.
Moreover, TBS manages a regularly updated list of program codes that groups each department’s main responsibilities and the programs under them.
The goal of this work is to review and, if needed, update these question sets so they better support data collection for CX and UX research (archetypes) and for strategic alignment with government priorities.
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- [x] Create a working [document](https://docs.google.com/document/d/1WNpNn98XLMRpatNo6ygklkmQuW2rDQanLP_vlbnfIyc/edit?tab=t.0)
- [x] Gather ressources (questions in the current UI, from UXR screener, program codes list)
- [x] Share for review
- [x] Update following review
- [ ] Prepare workshop for alignment on the questions
- [ ] Host a brainstorming session
- [ ] Co-propose final version, for UI update