[WIP] Update lycheeverse/lychee-action to version 2.8.0

[Copilot]

Thanks for the feedback on #154. I've created this new PR, which merges into #154, to address your comment. I will work on the changes and keep this PR's description up to date as I make progress.

Original PR: #154
Triggering comment (#154 (comment)):

@copilot how do we fix the breaking CI issue with eslint here?

Run npm ci
npm error code ERESOLVE
npm error ERESOLVE could not resolve
npm error
npm error While resolving: neostandard@0.12.2
npm error Found: eslint@10.0.1
npm error node_modules/eslint
npm error   dev eslint@"^10.0.1" from the root project
npm error   peer eslint@"^6.0.0 || ^7.0.0 || >=8.0.0" from @eslint-community/eslint-utils@4.9.0
npm error   node_modules/@eslint-community/eslint-utils
npm error     @eslint-community/eslint-utils@"^4.7.0" from @typescript-eslint/utils@8.38.0
npm error     node_modules/@stylistic/eslint-plugin/node_modules/@typescript-eslint/utils
npm error       @typescript-eslint/utils@"^8.13.0" from @stylistic/eslint-plugin@2.11.0
npm error       node_modules/@stylistic/eslint-plugin
npm error         @stylistic/eslint-plugin@"2.11.0" from neostandard@0.12.2
npm error         node_modules/neostandard
npm error     @eslint-community/eslint-utils@"^4.8.0" from eslint@10.0.1
npm error     4 more (eslint-plugin-es-x, eslint-plugin-n, ...)
npm error   5 more (@stylistic/eslint-plugin, eslint-compat-utils, ...)
npm error
npm error Could not resolve dependency:
npm error peer eslint@"^9.0.0" from neostandard@0.12.2
npm error node_modules/neostandard
npm error   dev neostandard@"^0.12.1" from the root project
npm error
npm error Conflicting peer dependency: eslint@9.39.3
npm error node_modules/eslint
npm error   peer eslint@"^9.0.0" from neostandard@0.12.2
npm error   node_modules/neostandard
npm error     dev neostandard@"^0.12.1" from the root project
npm error
npm error Fix the upstream dependency conflict, or retry
npm error this command with --force or --legacy-peer-deps
npm error to accept an incorrect (and potentially broken) dependency resolution.
npm error
npm error
npm error For a full report see:
npm error /home/runner/.npm/_logs/2026-03-01T12_08_11_546Z-eresolve-report.txt
npm error A complete log of this run can be found in: /home/runner/.npm/_logs/2026-03-01T12_08_11_546Z-debug-0.log
Error: Process completed with exit code 1.

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