How can doing this cannot affect your SEO?

If SEO's a concern, then there's nothing you can do about the LLM bit. Either put the website behind a login, or deal with robots sucking everything up.

Pre-LLMs, there were already many websites showing scraped versions of other people's sites, and ranking higher in search results.

Serve different content to non search engine bots

I often read that doing that was a big no-no as Google would flag your website as cheating. But that may be a SEO legend.