[Release 1.29] Improve tailscale test & add extra log in e2e tests

[manuelbuil]

Backports: #10119, #10145

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 37.41%. Comparing base (86ad488) to head (48d58a5).

Additional details and impacted files

@@                Coverage Diff                @@
##           release-1.29   #10212       +/-   ##
=================================================
- Coverage         50.21%   37.41%   -12.80%     
=================================================
  Files               158      155        -3     
  Lines             14038    13986       -52     
=================================================
- Hits               7049     5233     -1816     
- Misses             5663     7693     +2030     
+ Partials           1326     1060      -266     

Flag	Coverage Δ
e2etests	35.79% <ø> (-10.92%)	⬇️
inttests	32.78% <ø> (-4.40%)	⬇️
unittests	?

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