SEO is important for websites which for the record you 100% should not use Flutter for.
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.
Important for web apps or websites? There's a difference, a product's landing page will need SEO, definitely, but the app itself, ie app.example.com, likely does not need SEO. For example, an easy example is Figma. The landing page is built with HTML, CSS and JS, but the actual app itself is actually built with WASM [0], very similar to the canvas based implementation of Flutter apps.
I'm not sure there's a good distinction between web apps or websites today.
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.
True, if the app needs SEO, then yes it should be built with HTML, CSS and JS, and not Flutter which uses a canvas element. However, there are many apps where SEO is unneeded, such as Figma above (no one will search for your company's design files on Google) or other such corporate apps, and that's where Flutter comes in handy.
