Fix Branch Name logic for Dependabot and UpdateCLI pushes to k3s-io

[dereknola]

Proposed Changes

• Add more logic and checks around determining parent branch name for Docker Upgrade and Skew tests.
• Extend timeout for etcd split role docker test, 5 nodes takes more than 60s

Types of Changes

CI Test Fix

Verification

CI is green.
Note that this branch is specifically prefixed with dependabot to simulate a typical dependabot branch name.
Additionally, this PR is from a branch on k3s-io not from my personal fork, just like the bots make.
https://github.com/k3s-io/k3s/actions/runs/12039503425

Testing

Linked Issues

#11374

User-Facing Change

Further Comments

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 39.84%. Comparing base (b5e2fa7) to head (f81053e).
Report is 1 commits behind head on master.

❗ There is a different number of reports uploaded between BASE (b5e2fa7) and HEAD (f81053e). Click for more details.

HEAD has 11 uploads less than BASE

Flag	BASE (b5e2fa7)	HEAD (f81053e)
inttests	11	0

Additional details and impacted files

@@            Coverage Diff             @@
##           master   #11376      +/-   ##
==========================================
- Coverage   47.16%   39.84%   -7.32%     
==========================================
  Files         179      179              
  Lines       18600    18600              
==========================================
- Hits         8772     7412    -1360     
- Misses       8476    10096    +1620     
+ Partials     1352     1092     -260     

Flag	Coverage Δ
e2etests	34.24% <ø> (-8.01%)	⬇️
inttests	?
unittests	13.82% <ø> (ø)

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[cwayne18]

/trivy

[github-actions]

🌟 No High or Critical CVEs Found 🌟