feat(frontend): update settings form (#10628)

## Changes 🏗️

<img width="800" height="687" alt="Screenshot 2025-08-12 at 15 52 41"
src="https://github.com/user-attachments/assets/0d2d70b8-e727-428b-915e-d4c108ab7245"
/>

<img width="800" height="772" alt="Screenshot 2025-08-12 at 15 52 53"
src="https://github.com/user-attachments/assets/b9790616-3754-455e-b8f6-58cd7f6b5a18"
/>

Update the Account Settings ( `profile/settings` ) form so that:
- it uses the new Design System components
- it is split into 2 forms ( update email & notifications )
- the change password inputs have been removed instead we link to the
`/reset-password` page
- uses a normal API route and client query to update the email

This might fix as well an error we are seeing when updating email
preferences on dev. My guess is it is failing because previously it was
using a server action + supabase and it didn't have access to the
cookies auth 🍪

## Checklist 📋

### For code changes:
- [x] I have clearly listed my changes in the PR description
- [x] I have made a test plan
- [x] I have tested my changes according to the test plan:
  - [x] Navigate to `/profile/settings`
  - [x] Can update the email
  - [x] Can change notification preferences
  - [x] New E2E tests pass on the CI and make sense   

### For configuration changes:

None