I'm not sure how many people are asking ChatGPT for the best humidifier. And if they're asking Google and they look at the Gemini answer at the top, it seems to often be Gemini interpreting/summarizing the regular search results. Which means, just regular SEO strategy.
I don't think we're at a point where specifically targeting LLM searches is a productive strategy. Obviously that may change, but I don't think we're there yet.
The era of e.g. writing blog posts with some code snippets to try and get search traffic that converts into freelancing clients is waning (and the strategy wasn't super effective in the first place). That's always been better done via networking/social media/"thought leadership".
If you have like a SaaS CRM for Painters, the LLM is just another thing that your SEO will affect. If someone asks "How can I keep track of my painting clients?", the LLM is going to give some advice and probably point to some products (including hopefully yours). That remains largely unchanged, since LLM answers are not a substitute for a CRM (yet?)
There are a couple other companies in this space, with data focused on specific markets (US, Europe, etc). So you could find one that suits your geography.
Another thing you can do to find people interested in what you offer is following RSS feeds for keywords of your choice. HN RSS (https://hnrss.github.io) is particularly cool for HN! Tools like RSS Bridge (https://github.com/RSS-Bridge/rss-bridge) and Morss (https://github.com/pictuga/morss) can also help to get RSS feeds from websites that don't provide them and only provide a very trimmed down ones.
PPC(if you have budget)
YouTube(you can see a list of YouTube videos on top search positions)
Sponsoring(podcasts,newsletters)
Something about the URL, or perhaps a super-cookie, or some such will then give OpenAI, or whoever, a kickback.