I'm sorry to hear that. Unfortunately, I'm not up to speed on troubleshooting the Arduino Cloud firmware update system. All I know about it is what was explained in the forum topic I linked to above.
I think the easiest way to do it will be to download the test build for your operating system from the pull request where the Arduino IDE developer is doing the work to update the firmware updater in the Arduino IDE here:
https://github.com/arduino/Arduino/pull/11496#issuecomment-834382462
Just download the file, extract it, then run the arduino executable in the extracted folder. From there, you can just do the standard Arduino IDE firmware update process. After updating the firmware, you are welcome to go back to using Arduino IDE 1.8.13 or Arduino Cloud Editor, or whatever you prefer. The test build of the IDE is just a convenient way to get the latest available firmware.
Another option is the "FirmwareUploader" tool:
This is a command line tool. Unfortunately, it looks like the latest NINA version it provides is 1.4.4.
One thing important to note: The outdated firmware message you're seeing is only meant to be a helpful reminder to keep your NINA firmware up to date. Most often, the previous firmware versions work just fine. So don't get so uptight about this message unless you have good reason to believe that you really do need an update.