Browser+JSON flow feature parity with Browser+HTML flow

[hperl]

Preflight checklist

• I could not find a solution in the existing issues, docs, nor discussions.
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• I have read and am following this repository's Contribution Guidelines.
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Describe your problem

Using the browser+JSON flows (i.e., browser API + accept JSON) is currently lacking a couple of features:

• After a successful OIDC login the response does not contain the correct callback URL to follow up with the consent. Draft PR here: fix: accept OIDC login request in browser+JSON login flow #3271
• The value of the ory_kratos_continuity cookie is not returned as part of the JSON response when submitting a login/registraton flow.

Describe your ideal solution

Implement the missing features.

Workarounds or alternatives

User Browser+HTML flow

Version

master

Additional Context

No response

[BrandonNoad]

I wanted to add a bit more context.

After a successful OIDC login the response does not contain the correct callback URL to follow up with the consent. Draft PR here: #3271

In the scenario above, the user is signing in to a third-party service and Ory is acting as the OAuth/OIDC provider.

The value of the ory_kratos_continuity cookie is not returned as part of the JSON response when submitting a login/registraton flow.

In the scenario above, the user is using Ory's "Social Sign-In" feature to sign in to the application. Ory is acting as the OAuth/OIDC client.

The two scenarios could also be combined together in a single flow.