To create a SPFx solution using version 1.13 or newer, install Yeoman v4+.

As of SPFx v1.13, local workbench is no longer supported. This is a game changer, as debugging requires slightly more effort right now.

To quickly get things working and ready for debugging, I'm using SharePoint Framework - Visual Studio Code Debug Configuration Extension. It's an absolute life saver.

After installing the extension:

open the .vscode\launch.json file. You will see one default "Hosted workbench" configuration,
click on "Add Configuration" button in the bottom right corner
this will open a dropdown within the configurations node: The ones starting with SPFx: come from the SharePoint Framework - Visual Studio Code Debug Configuration Extension extension.
choose the configuration matching your extension type
the newly created debug configurations need to be updated; see Updating Debug Configurations below
run gulp serve --nobrowser

Updating Debug Configurations

The url parameters are documented in Debug extensions by manually building the debug URL. There's a gotcha: the fieldName parameter of fieldCustomizers seems to be a display name, and not an internal name of the field as stated in the documentation.
Update the whole url. The extension gives you https://contoso.sharepoint.com/documents, which should be changed to sth like https://your-SharePoint-teanant.sharepoint.com/sites/your-site/Shared%20Documents or https://your-SharePoint-teanant.sharepoint.com/sites/your-site/Lists/your-list.
You can choose the browser you are using, e.g. "type": "chrome" or "type": "msedge". You don't need to install any debugger extensions. It used to be the case but Visual Studio Code now has a JavaScript Debugger.
If you see Missing property "version". warning, add "version": "dev".
In case you have a monorepo, you will see a number of .vscode\launch.json files, and only one will be used for debugging. You won't go wrong if you access your launch.js from "Run and Debug" > "Open launch.json":

You should end up with something like:

launch.json

{
  "version": "0.2.0",
  "configurations": [
    {
      "name": "ListViewCommandSet debug",
      "type": "chrome",
      "request": "launch",
      "url": "https://your-SharePoint-teanant.sharepoint.com/sites/your-site/Shared%20Documents?loadSPFX=true&debugManifestsFile=https://localhost:4321/temp/manifests.js&customActions={\"00000000-0000-0000-0000-000000000000\":{\"location\":\"ClientSideExtension.ListViewCommandSet.CommandBar\"}}",
      "webRoot": "",
      "sourceMaps": true,
      "sourceMapPathOverrides": {
        "webpack:///../../../src/*": "/src/*",
        "webpack:///../../../../src/*": "/src/*",
        "webpack:///../../../../../src/*": "/src/*"
      },
      "runtimeArgs": [
        "--remote-debugging-port=9222"
      ]
    },
    {
      "name": "FieldCustomizer debug",
      "version": "dev",
      "type": "msedge",
      "request": "launch",
      "url": "https://your-SharePoint-teanant.sharepoint.com/sites/your-site/Lists/your-list?loadSPFX=true&debugManifestsFile=https://localhost:4321/temp/manifests.js&fieldCustomizers={\"FieldName\":{\"id\":\"00000000-0000-0000-0000-000000000000\",\"properties\":{\"prop1\":\"val1\"}}}",
      "webRoot": "",
      "sourceMaps": true,
      "sourceMapPathOverrides": {
        "webpack:///../../../src/*": "/src/*",
        "webpack:///../../../../src/*": "/src/*",
        "webpack:///../../../../../src/*": "/src/*"
      },
      "runtimeArgs": [
        "--remote-debugging-port=9222"
      ]
    },
    {
      "name": "Hosted workbench",
      "version": "dev",
      "type": "chrome",
      "request": "launch",
      "url": "https://your-SharePoint-teanant.sharepoint.com/sites/your-site/_layouts/workbench.aspx",
      "webRoot": "${workspaceRoot}",
      "sourceMaps": true,
      "sourceMapPathOverrides": {
        "webpack:///.././src/*": "${webRoot}/src/*",
        "webpack:///../../../src/*": "${webRoot}/src/*",
        "webpack:///../../../../src/*": "${webRoot}/src/*",
        "webpack:///../../../../../src/*": "${webRoot}/src/*"
      },
      "runtimeArgs": [
        "--remote-debugging-port=9222",
        "-incognito"
      ]
    }
  ]
}

Seems like a lot? It's totally worth it =) From now on, all your debug configurations are ready whenever you need them:

UPDATE 31.01.2022:

Testing localized solutions

In order to test localized solutions without switching profile settings, simply add ?forceLocale parameter:

launch.json

{
    "name": "Hosted workbench English",
    "url": "https://your-SharePoint-teanant.sharepoint.com/sites/your-site/_layouts/workbench.aspx?forceLocale=en-EN",
    ...
},
{
    "name": "Hosted workbench German",
    "url": "https://your-SharePoint-teanant.sharepoint.com/sites/your-site/_layouts/workbench.aspx?forceLocale=de-DE",
    ...
}

Debugging SPFx 1.13+ solutions

Updating Debug Configurations

launch.json

Testing localized solutions

launch.json