When I look up things, I do not use my vault for it. Instead, I’m using a search engine. It would be nice, if related notes to a search could be embedded into the search results.
Easiest but not quite the same: searching in Spotlight gives full-text search results for local files (not limited to Obsidian vault, with no preview) and suggestions for web searches.
I suspect Alfred and other fancy Spotlight replacements might get you closer to what you want, but I haven’t used them.
You could make a Shortcut that searches both Obsidian (using Obsidian URI) and the web. If you also use third-party window management tools like Magnet and Warp, it might be able to put Obsidian and the browser side-by-side for you.
If you’re not on Mac, these may help you find similar apps/approaches.