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Samsung Internet Browser is available for the Galaxy Watch. The only other one I've tried is Gear Browser (also by Samsung), but since it's the latest browser made by Samsung, Samsung Internet is probably your best bet.
"Gear Browser" by Changyong Jeon is what I'm currently using. It works pretty well and has a good interface for accessing bookmarks. I usually only use the browser for things like flight or transit status and it works great for those things.
I use Samsung Internet just for news headlines, via a bookmark, using Easy view mode. Gives a basic text view with a photo or two so I can catch up on the latest news quickly. Works well on such a small screen. Wouldn't really bother for anything requiring a full webpage.
And this is a much better experience than the Flipboard news briefing which is rubbish.