ci: Use publish function from @tanstack/config

[lachlancollins]

This replaces the local publish function with that from https://github.com/TanStack/config/blob/main/src/publish/index.js

[codesandbox-ci]

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[codecov-commenter]

Codecov Report

Attention: 71 lines in your changes are missing coverage. Please review.

Comparison is base (c2f9957) 84.55% compared to head (4fb37fc) 87.74%.
Report is 109 commits behind head on main.

Files	Patch %	Lines
...ckages/solid-form/src/tests/createField.test-d.tsx	0.00%	26 Missing ⚠️
packages/form-core/src/FormApi.ts	91.04%	12 Missing ⚠️
packages/react-form/src/validateFormData.ts	16.66%	8 Missing and 2 partials ⚠️
packages/form-core/src/utils.ts	89.47%	6 Missing ⚠️
packages/form-core/src/FieldApi.ts	95.60%	4 Missing ⚠️
packages/form-core/src/mergeForm.ts	85.71%	3 Missing ⚠️
packages/react-form/src/useField.tsx	85.71%	2 Missing ⚠️
packages/react-form/src/useTransform.ts	0.00%	2 Missing ⚠️
packages/vue-form/src/useForm.tsx	66.66%	2 Missing ⚠️
packages/react-form/src/useIsomorphicEffectOnce.ts	94.11%	1 Missing ⚠️
... and 3 more

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Additional details and impacted files

@@            Coverage Diff             @@
##             main     #552      +/-   ##
==========================================
+ Coverage   84.55%   87.74%   +3.18%     
==========================================
  Files           9       31      +22     
  Lines         395      816     +421     
  Branches      109      182      +73     
==========================================
+ Hits          334      716     +382     
- Misses         52       95      +43     
+ Partials        9        5       -4     

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