Run using Node.js 16, bump NPM & GHA deps

[GaryGSC]

This is considered breaking because of the change to using: 'node16' (since that requires a newer runner version). We're basically all using ubuntu-latest over at BYU, but we have some external users. Assuming this gets approval, I say we plan on releasing it as v2.0.0.

I was able to update most of the dependencies. This is what's left when I run yarn outdated:

Package                   Current Wanted  Latest  Package Type    URL
@types/node               16.18.3 16.18.3 18.11.9 devDependencies https://github.com/DefinitelyTyped/DefinitelyTyped/tree/master/types/node
@typescript-eslint/parser 2.34.0  2.34.0  5.42.0  devDependencies https://github.com/typescript-eslint/typescript-eslint#readme
eslint                    5.16.0  5.16.0  8.26.0  devDependencies https://eslint.org
eslint-plugin-github      2.0.0   2.0.0   4.4.0   devDependencies https://github.com/github/eslint-plugin-github#readme
eslint-plugin-jest        22.21.0 22.21.0 27.1.3  devDependencies https://github.com/jest-community/eslint-plugin-jest#readme
eslint-plugin-prettier    3.4.1   3.4.1   4.2.1   devDependencies https://github.com/prettier/eslint-plugin-prettier#readme
Done in 0.78s.

The ESLint stuff is a mess of peer dependencies and rule changes that don't play nicely with our current .eslintrc.json.

[GaryGSC]

The main goals of this PR are to remove deprecation warnings and to resolve about a year and a half of technical debt.