As a convenient time-saver, Safari will automatically detect and fill SMS-based two-factor authentication codes received in Messages. This feature allows for faster login completion—no code retrieval necessary.
Unfortunately, Apple does not allow additional developers access to such codes in Messages. So for other web browsers—like Google Chrome, Firefox, Brave, or Arc—code auto-filling is not an option.
Thankfully, Messages itself recognizes verification codes, marking them with an underline. So rather than having to manually transcribe a code, simply Control-click the underlined numbers and choose Copy Code. Then, press Command-V to paste the code in the web browser of your choice. And though not all websites accept pasted codes, most websites will, even if they present a custom interface.