Hi
It looks to me as if the spell check attribute is not a feature of CSS - only HTML which is to be expected since CSS should change appearance and layout but not functionality or content although that line has been blurred a little.
My test word in the text area I am editing right now is below.
baad
I added spellcheck=“false” in the HTML for this editor whilst I was using it using Mozilla developer tools and observed that the spell checker no longer detected the word baad. Of course this was only a temporary change and one that only affects me locally.
If you can find out how to permanently change the HTML for the editor element in Tiddlywiki it might be the solution for you.
Regards the CSS route, it would seem there are experiments in this direction but it seems that browser support is currently not there. This fix would of course merely be a method for turning off the visual indications of a mis spelling but would not turn off the spell checker itself.