Recommended size of icon for Google Chrome Extension

To elaborate on ExpertSystem's answer, here is an example manifest excerpt with all of the image sizes:

  "browser_action": {
    "default_icon": {
      "19": "images/icon19.png",
      "38": "images/icon38.png"
    },
    "default_popup": "popup.html"
  },
  "icons": { "16": "images/icon16.png",
           "48": "images/icon48.png",
          "128": "images/icon128.png" }, ...

Notice how the 19/38 icons are for the browser action, and the 16/48/128 are at the icons level.

I think it is best therefore to create the image as a vector graphic (e.g. svg file) and then save to a bitmap (e.g. png file) for each of the sizes.

Both are correct ! They are for different sections/features:

The former refers to the browser-action icon (displayed on the top-right corner of your browser-window, next to the address bar). It is only displayed if your extension registers a browser-action.

The latter refers to icons used throughout the extension and browser, as is explained quite clearly in the link you provide:
_{(emphasis mine)}

One or more icons that represent the extension, app, or theme. You should always provide a 128x128 icon; it's used during installation and by the Chrome Web Store. Extensions should also provide a 48x48 icon, which is used in the extensions management page (chrome://extensions). You can also specify a 16x16 icon to be used as the favicon for an extension's pages. The 16x16 icon is also displayed in the experimental extension infobar feature.

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BTW, that second link mentions icon as the property name, which was replaced in Manifest v2 by default_icon.
_{("Migration to Manifest v2" guide)}