docs: complete design-partner intake

[yhay81]

What changed

• add hayate-admin and hayate-htmx to the design-partner package selector
• add a regression test requiring the full current public package set
• retain owner-external, privacy, and measurement confirmations as tested contracts

Why

The v1 design-partner program was already public, but its intake form lagged the released ecosystem. Operational-admin and hypermedia users could not accurately describe the package surface they intended to evaluate.

Impact

External applicants can now select every current first-party Hayate package without using free-form workarounds. No application data, selection policy, or privacy boundary changes.

Validation

• python3 -m unittest discover -s tests
• python3 scripts/check_evidence.py
• python3 scripts/export_compatibility.py --check
• python3 scripts/export_profile.py --check
• python3 scripts/check_links.py
• bash scripts/check_start.sh (including 17 generated-application tests)
• PyYAML parse, Ruff check/format, live form URL, and help wanted label checks