2022-02-17 UPDATE: See this very primitive proof of concept.
BASIC Anywhere Machine's BASIC implementation includes the functions SetLocalStorageItem(key,value) and GetLocalStorageItem(key).
With the SetLocalStorageItem statement, a BASIC Anywhere Machine program can output processing results to browser local storage.
A TiddlyWiki, via a GetLocalStorageItem javascript macro, can retrieve values from local storage.
The only caveat: a TiddlyWiki and a BASIC Anywhere Machine program must reside in the same domain (i.e. have "same site origin) to access the same area of browser local storage.
So as good as TiddlyWiki au naturel is, BASIC Anywhere Machine can be used as a scripting tool for a TiddlyWiki instance, very convenient when there is some heavy-duty processing that needs to be done and BASIC makes that a breeze !