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.
I created the open source Vault Lens Extension (formerly Obsidian Browser Search) for exactly the purpose that @veto is talking about. When you are searching for something on the web it fetches matching notes form you Obsidian Vault and embedds them in the search results. By now a lot of different search engines are supported.
The extension brings many more features to the table, such as:
Note Recall / URL matching: resurface notes when you browse pages that you have already taken notes about
Note Preview and Editing: Open and view your notes in the browser and conveniently change the content
Page Notes (inspired and compatible with Obsidian Web): receive customizable notifications messages when you browse pages that have dedicated notes in your vault