Allow the Rails cookie to be used for API authentication

Makes the Rails cookie into a valid authentication token for the Grape
API, and uses it instead of token authentication in frontend code that
uses the API.

Rendering the private token into client-side javascript is a security
risk; it may be stolen through XSS or other attacks. In general,
re-using API code in the frontend is more desirable than implementing
endless actions that return JSON.

Closes #18302

See merge request !1995
Signed-off-by: Rémy Coutable <remy@rymai.me>