webpack can't find module vscode, 'vscode-debugadapter', and 'vscode-debugprotocol'

I'm following the guide bellow as suggested by vscode as my extension is getting apparently large: https://code.visualstudio.com/api/working-with-extensions/bundling-extension

I followed the instructions verbatim, and copied the webpack.config.js exactly as it is on that page. Running the npm run webpack as instructed results in the following errors:

> npm run webpack

> vsc-octave-debugger@0.3.18 webpack /Users/paulo/dev/javascript/vscOctaveDebugger
> webpack --mode development

Hash: 8845934a16e1bf0af4ce
Version: webpack 4.41.5
Time: 1809ms
Built at: 02/02/2020 5:36:33 PM
           Asset      Size  Chunks                   Chunk Names
    extension.js  11.6 KiB    main  [emitted]        main
extension.js.map  9.53 KiB    main  [emitted] [dev]  main
Entrypoint main = extension.js extension.js.map
[./src/Constants.ts] 1.06 KiB {main} [built]
[./src/extension.ts] 2.33 KiB {main} [built] [2 errors]
[vscode] external "vscode" 42 bytes {main} [built]

ERROR in /Users/paulo/dev/javascript/vscOctaveDebugger/src/OctaveDebugger.ts
[tsl] ERROR in /Users/paulo/dev/javascript/vscOctaveDebugger/src/OctaveDebugger.ts(14,8)
      TS2307: Cannot find module 'vscode-debugadapter'.

ERROR in /Users/paulo/dev/javascript/vscOctaveDebugger/src/OctaveDebugger.ts
[tsl] ERROR in /Users/paulo/dev/javascript/vscOctaveDebugger/src/OctaveDebugger.ts(16,31)
      TS2307: Cannot find module 'vscode-debugprotocol'.

(many similar errors...)

ERROR in /Users/paulo/dev/javascript/vscOctaveDebugger/src/Utils/fsutils.ts
[tsl] ERROR in /Users/paulo/dev/javascript/vscOctaveDebugger/src/Utils/fsutils.ts(2,31)
      TS2307: Cannot find module 'vscode-debugprotocol'.
npm ERR! code ELIFECYCLE
npm ERR! errno 2
npm ERR! vsc-octave-debugger@0.3.18 webpack: `webpack --mode development`
npm ERR! Exit status 2
npm ERR! 
npm ERR! Failed at the vsc-octave-debugger@0.3.18 webpack script.
npm ERR! This is probably not a problem with npm. There is likely additional logging output above.

npm ERR! A complete log of this run can be found in:
npm ERR!     /Users/paulo/.npm/_logs/2020-02-02T08_47_30_676Z-debug.log

All these modules actually exist in the node_modules and I did run npm i before. The extension works fine without webpack. Any ideas on how to fix this, or at least understand why webpack can't find the modules? Thanks!

I've created a patch that can be used with the example on that page to reproduce the issue: https://pastebin.com/peqvJ1Wt