Do I need MacOS Big Sur to update my iPhone 8 to iOS 14.3

In answer to your question, no you don't. You might need to update a small piece of software to do so however. You might have come across the message in the following How To document:

https://support.apple.com/en-us/HT208831

If you see "Software update is required to connect to your iOS device" on your iPhone, iPad, or iPod touch

If you see the message, go ahead and perfom the update. Download and install should take about 5 minutes and it will not require a restart of your Mac. Make sure you're using the latest version of iTunes as well

Why not update the iPhone 8 via the update facility on the phone without dealing with macOS at all?