Why can’t I see the Apple Watch icon on my iPhone 8 Plus?

if you mean the watch app then it can be deleted from the phone

if you have then you can read about restoring it here Delete built-in Apple apps on your iOS 12, iOS 13, or iPadOS device or Apple Watch - Apple Support

what happens if you use search to look for it?

if you are unsure how then read

Use Search on your iPhone, iPad, or iPod touch - Apple Support

then it's likely in some folder somewhere or the folder layout gotten corrupt and does not display it you can try

to reset the home screen layout

If I reset home screen layout what will t… - Apple Community

and see if it does not end up on one of the home screens then