fix: publish to dist branch

[ReenigneArcher]

Description

Publish to dist branch instead of directly to gh-pages. This allows other services, such as jsdelivr to also tap into the api files.

Screenshot

Issues Fixed or Closed

Roadmap Issues

Type of Change

• feat: New feature (non-breaking change which adds functionality)
• fix: Bug fix (non-breaking change which fixes an issue)
• docs: Documentation only changes
• style: Changes that do not affect the meaning of the code (white-space, formatting, missing semicolons, etc.)
• refactor: Code change that neither fixes a bug nor adds a feature
• perf: Code change that improves performance
• test: Adding missing tests or correcting existing tests
• build: Changes that affect the build system or external dependencies
• ci: Changes to CI configuration files and scripts
• chore: Other changes that don't modify src or test files
• revert: Reverts a previous commit
• BREAKING CHANGE: Introduces a breaking change (can be combined with any type above)

Checklist

• Code follows the style guidelines of this project
• Code has been self-reviewed
• Code has been commented, particularly in hard-to-understand areas
• Code docstring/documentation-blocks for new or existing methods/components have been added or updated
• Unit tests have been added or updated for any new or modified functionality

AI Usage

• None: No AI tools were used in creating this PR
• Light: AI provided minor assistance (formatting, simple suggestions)
• Moderate: AI helped with code generation or debugging specific parts
• Heavy: AI generated most or all of the code changes

[sonarqubecloud]

Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud