Adding simple embed opportunities

Full warning this is part because I struggle to come to t3 chat as it's not in places I want to use it.

However to change that a simple embed system could help with that. This can range from a simple text box “search” like option that then brings you to t3 with a new chat and your message, to being able to easily embed it anywhere.

Could easily see with an embed the opportunity to say put it in my vscode, or on my custom home pages. Just would be nice to lean a little heavier into the dev friendly.

I'm thinking similar to the YouTube video embedding system which even when I was a child I enjoyed embedding places.

Also could be a nice form of revenue just saying, if open source projects could embed a chat bot into their sites with a system prompt, users would have to be subscribed but at least the project doesn't inherent the costs of maintaining a chat bot. And since Theo seems anti ads in t3 chat direct to site traffic doesn't matter as much(links possibly more so if you're going off old SEO metrics)

Just idea but a thought to think on