fix: remove unnecessary gh workflow run

[JoshuaKGoldberg]

PR Checklist

• Addresses an existing open issue: fixes 🐛 Bug: gh workflow trigger still in release.yml template #863
• That issue was marked as status: accepting prs
• Steps in CONTRIBUTING.md were taken

Overview

Removing this aligns release.yml to the template, yay!

[codecov]

Codecov Report

Merging #868 (09f1412) into main (dcc6ad4) will decrease coverage by 0.01%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main     #868      +/-   ##
==========================================
- Coverage   92.50%   92.50%   -0.01%     
==========================================
  Files          89       89              
  Lines        4535     4534       -1     
  Branches      322      322              
==========================================
- Hits         4195     4194       -1     
  Misses        339      339              
  Partials        1        1              

Flag	Coverage Δ
create	70.76% <100.00%> (-0.01%)	⬇️
initialize	35.01% <0.00%> (+<0.01%)	⬆️
migrate	70.20% <100.00%> (-0.01%)	⬇️
unit	55.01% <0.00%> (+0.01%)	⬆️

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Files Changed	Coverage Δ
src/steps/writing/creation/dotGitHub/workflows.ts	88.29% <100.00%> (-0.05%)	⬇️

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[github-actions]

🎉 This is included in version v1.32.0 🎉

The release is available on:

• GitHub releases
• npm package (@latest dist-tag)

Cheers! 📦🚀