Properly remove all deprecations actions-rs#224

This PR supersedes actions-rs#220 and actions-rs#222 by applying both fixes at once
Fixes actions-rs#219
Fixes actions-rs#221

You can now use this action (and cargo) without deprecations by using a workflow similar to this:

on: [push]

name: build

jobs:
  check:
    name: Rust project
    runs-on: ubuntu-latest
    steps:
      - uses: actions/checkout@v3
      - name: Install latest nightly
        uses: ThexXTURBOXx/toolchain@master
        with:
            toolchain: nightly
            override: true
            components: rustfmt, clippy

      # `cargo check` command here will use installed `nightly`
      # as it is set as an "override" for current directory

      - name: Run cargo check
        uses: richb-hanover/cargo@master
        with:
          command: check