what macOS upgrades are compatible with my high sierra 10.13.6

Sirmiq wrote:

A Mac book pro 2010

that model (now 13 years old) is supported through 10.13 High Sierra.

Its hardware is considered inadequate to support more modern versions of MacOS.

Your Mac continues to be able to do everything it could do the day you took it out of the box. And because Apple has released many improved versions of MacOS since then, at no additional cost to you, it likely can do a whole lot more.

Apple's policy has been to continue to provide Security Updates for the current version of MacOS AND the two previous versions. Nothing falls off a cliff and stops working because a new version of MacOS is issued and you can not run it on your older Mac.

They just stopped giving you free upgrades.

If you are not satisfied with this, it is NOT because anyone has taken anything away -- it is because your desires have expanded while you computer is no longer adding capabilities every year, for free.

To add just a bit to the excellent replies already posted, you really can't upgrade your 13 year old MacBook Pro past the High Sierra you already have.

If it's just a particular website that's telling you an update is needed, then I'd suggest using an alternative browser, like Firefox, Brave, DuckDuckGo, or Chrome. I say this because there are a few websites that are telling users they need to update their Safari...but Safari can only be updated by updating the MacOS...and your MacOS can't be updated any more.

Of course, another option would be to start shopping for a new(er) Mac.

What is your laptop (e.g., MacBook, MacBook Air, MacBook Pro) and what model year is it (other of those things are available at Apple menu >About This Mac)?