For new features file an issue. For bugs, file an issue and optionally file a PR with a failing test.
To execute the tests run pnpm test.
To learn about ESLint plugin development see the relevant section of the ESLint docs. You can also checkout the typescript-eslint repo which has some more information specific to TypeScript.
In order to know which AST nodes are created for a snippet of TypeScript code you can use AST explorer with options JavaScript and @typescript-eslint/parser.
Publishing is handled by semantic release - there shouldn't be any need to publish manually.