test: run Playwright in CI

[hperl]

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
  [email protected]) 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

Merging #3259 (fa72f1a) into master (6db70a8) will decrease coverage by 0.03%.
The diff coverage is 72.50%.

❗ Current head fa72f1a differs from pull request most recent head a258713. Consider uploading reports for the commit a258713 to get more accurate results

@@            Coverage Diff             @@
##           master    #3259      +/-   ##
==========================================
- Coverage   78.14%   78.11%   -0.03%     
==========================================
  Files         324      324              
  Lines       20760    20754       -6     
==========================================
- Hits        16222    16213       -9     
  Misses       3333     3333              
- Partials     1205     1208       +3     

Impacted Files	Coverage Δ
selfservice/flow/login/hook.go	84.67% <0.00%> (ø)
selfservice/flow/registration/error.go	68.11% <0.00%> (ø)
selfservice/flow/registration/hook.go	71.73% <0.00%> (ø)
selfservice/sessiontokenexchange/persistence.go	100.00% <ø> (ø)
session/manager.go	100.00% <ø> (ø)
selfservice/hook/session_issuer.go	80.00% <40.00%> (+0.58%)	⬆️
persistence/sql/persister.go	69.89% <50.00%> (-0.90%)	⬇️
selfservice/flow/login/error.go	70.31% <50.00%> (+0.47%)	⬆️
selfservice/flow/login/handler.go	78.82% <60.00%> (-1.49%)	⬇️
persistence/sql/persister_sessiontokenexchanger.go	97.33% <100.00%> (+0.55%)	⬆️
... and 2 more

... and 1 file with indirect coverage changes