Testing: Transition away from ESLint valid-jsdoc rule

[aduth]

Related: eslint/eslint#11145
Related: https://eslint.org/blog/2018/11/jsdoc-end-of-life

Per the above links, ESLint is undergoing a deprecation of built-in support for JSDoc. As such, we should consider preemptively switching to another plugin, such as eslint-plugin-jsdoc. As a side-effect, this could greatly expand the specific enforcement we'd like to see, in order to more closely align with JavaScript Documentation Standards.

I came across the discovery of the deprecation as a result of its buggy behavior (example), which can be further motivation for expediting a transition.

[aduth]

Perhaps of interest to you @nosolosw , given your work at #13329.

[oandregal]

Just noting that as doctrine will be no longer developed, we also need to update docs/tool, where it is used to create this handbook section.