ci: Adjust release to use app token to allow rules bypass

[davelosert]

Changing the release process here a little bit in order for me to be able to enforce pull requests for all changes by a repo rule, but allow the release process to still commit the dist folder.

[github-actions]

Coverage Report for Mock Reports (./test/mockReports)

Status	Category	Percentage	Covered / Total
🔵	Lines	41.37%	60 / 145
🔵	Statements	41.33%	62 / 150
🔵	Functions	62.06%	18 / 29
🔵	Branches	39.65%	23 / 58

File Coverage

No changed files found.

Generated in workflow #710

[github-actions]

Coverage Report for Root

Status	Category	Percentage	Covered / Total
🔵	Lines	44.06%	293 / 665
🔵	Statements	44.06%	293 / 665
🔵	Functions	75%	15 / 20
🔵	Branches	91.13%	72 / 79

File Coverage

File	Stmts	% Branch	% Funcs	% Lines	Uncovered Lines
Unchanged Files
src/icons.ts	100%	100%	100%	100%
src/index.ts	0%	0%	0%	0%	1-6, 10-13, 15, 17-27, 29, 31-34, 36-43, 45-55, 57-59, 61-74, 76-77, 79-81, 83-84, 86-93, 95-99, 101-107
src/writeSummaryToPR.ts	0%	0%	0%	0%	1-2, 4-7, 10-14, 18, 20, 22, 24, 27-31, 33-36, 38-43, 45-60, 62-74, 76-81, 83-84, 86-91, 93-98, 100, 102-107, 109-114, 117-122, 125-127, 130-133, 135-140, 142-143, 145-154, 156-169
src/inputs/FileCoverageMode.ts	100%	100%	100%	100%
src/inputs/getPullChanges.ts	0%	0%	0%	0%	1-4, 8-10, 12-14, 17-19, 21-25, 27-29, 31-36, 38-39, 41-58, 60-64
src/inputs/getViteConfigPath.ts	97.95%	87.5%	100%	97.95%	47
src/inputs/options.ts	0%	0%	0%	0%	1-5, 7, 9, 11-12, 14-21, 23-30, 32, 35-42, 45-51, 53-63
src/inputs/parseCoverageThresholds.ts	100%	100%	100%	100%
src/inputs/parseJsonReports.ts	0%	0%	0%	0%	1-4, 8-14, 16-24, 28-29, 32-34, 36-44, 48-52
src/report/generateFileCoverageHtml.ts	100%	100%	100%	100%
src/report/generateFileUrl.ts	92.85%	50%	100%	92.85%	6
src/report/generateHeadline.ts	100%	100%	100%	100%
src/report/generateSummaryTableHtml.ts	100%	100%	100%	100%
src/report/getUncoveredLinesFromStatements.ts	100%	100%	100%	100%

Generated in workflow #710