## Context
For the Vercel integration flow (e.g "Deploy with Vercel" button on GH)
If an organization has no projects, there currently isn't a way to
create a project and connect it in the same session - users can only hit
"Skip".
This addresses that by directing users to the /deploy-button/new-project
route in this scenario
<img width="505" height="539" alt="image"
src="https://github.com/user-attachments/assets/6cc85030-42c7-4e58-b4b3-cb8ac0f5da9e"
/>
## Other changes involved
- Also separates `ProjectLinker` into smaller components - preference
for avoiding declaration of components within a component
## To test
I'm not sure if this can be tested on staging to be honest, but
otherwise we can give it a go on production after the changes are
through, as this doesn't change any existing logic to the usual "Connect
project" flow
I did try clicking the "Deploy with Vercel" button on a repo, and just
changing the URL to the staging URL at the Supabase step - seems to work
<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit
## Summary
* **UI Improvements**
* Streamlined the Vercel/GitHub project-linking step while keeping the
same create/connect/skip flow, including the searchable project picker,
branding/status indicators, and the feature-flagged “create new project”
option.
* On the Vercel choose-project step, the default selection now reflects
the current project context.
* **Bug Fixes / Tests**
* Improved Vercel install routing query handling to preserve
deploy-button configuration when present, with updated automated test
coverage.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->
---------
Co-authored-by: Danny White <3104761+dnywh@users.noreply.github.com>
