Flutter is a great fit for applications which (and I say this as someone who did SEO for fortune 500s for many years) aren’t really all that relevant for SEO purposes and are difficult to index at best.
But the short answer to your question is the accessibility object model API is what gets used to surface relevant information that could be used by search engines along with all the other things that have nothing to do with the stuff that sits inside your body tags. Like it wouldn’t actually be that different IRL.
https://www.figma.com/blog/webassembly-cut-figmas-load-time-...
Would you consider Instagram or Twitter a website or a web app?
If I type 'IG ${username}' or 'Twitter ${username}' or '@${username}' in a search engine, you should expect what is to be expected within the first result.