fix: add continue with only for json browser requests

[aeneasr]

Related issue(s)

Checklist

• I have read the contributing guidelines.
• I have referenced an issue containing the design document if my change
  introduces a new feature.
• I am following the
  contributing code guidelines.
• I have read the security policy.
• I confirm that this pull request does not address a security
  vulnerability. If this pull request addresses a security vulnerability, I
  confirm that I got the approval (please contact
  security@ory.sh) from the maintainers to push
  the changes.
• I have added tests that prove my fix is effective or that my feature
  works.
• I have added or changed the documentation.

Further Comments

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 78.32%. Comparing base (6016cc8) to head (edc01a5).
Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4002      +/-   ##
==========================================
- Coverage   78.35%   78.32%   -0.04%     
==========================================
  Files         369      369              
  Lines       25967    25967              
==========================================
- Hits        20347    20339       -8     
- Misses       4073     4080       +7     
- Partials     1547     1548       +1     

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