[Tech] Create API for saving research

[mariojsnunes]

Is your feature request related to a problem? Please describe.
Create an API using Remix routing.
Should be done by creating the action routes:

• api.research.ts
• api.research.$id.ts (edit)

The API must validate the authenticated user.

Additional context
This is part of the effort to decouple the firebase from the client to make it easier for a Supabase migration.
And also improve codebase maintainability.

Blocked by:

1. [Tech] Server-side Auth #3960