Make my watch work without my cellular phone

The first hyperlink in the 'Use Apple Watch with a cellular network' section of:

Use Apple Watch with a cellular network - Apple Support

says there is a Apple Watch series 3 with GPS+Cellular

"With Apple Watch with cellular and a cellular connection to the same carrier used by your iPhone, you can make calls, reply to messages, use Walkie-Talkie, stream music and podcasts, receive notifications, and more, even when you don’t have your iPhone or a Wi-Fi connection."

tarashea wrote:

I want my watch to work without my phone or when it’s away from my phone

That is not possible, since there are no Cellular versions of the Apple Watch Series 3. Apple Watch - Compare Models lists other versions which have cellular capability.

Concur with your observation. It's a rabbit hole IMHO. If I follow the Apple Watch - Compare Models link it never reveals a cellular model.

In any event, apparently the OP does not have a cellular version, and should consider purchasing one.

This requires you to pay attention to your purchase version when you buy a watch.