There are a few ways to do this that we've tried, namely Extractus[0] and dom-to-semantic-markdown[1].
Internally we use Apify[2] and Firecrawl[3] for Magic Loops[4] that run in the cloud, both of which have options for simplifying pages built-in, but for our Chrome Extension we use dom-to-semantic-markdown.
Similar to the article, we're currently exploring a user-assisted flow to generate XPaths for a given site, which we can then use to extract specific elements before hitting the LLM.
By simplifying the "problem" we've had decent success, even with GPT-4o mini.
[0] https://github.com/extractus
[1] https://github.com/romansky/dom-to-semantic-markdown