Margin issues of headers and footers in Fullwidth environment for even pages

[Phil8544]

The main problem is presented and illustrated in the following question:
https://tex.stackexchange.com/questions/572059/how-to-modify-margins-of-header-and-footer-in-a-new-environment
The use of \newgeometry makes it possible to solve the layout problems of the body of the text in full width mode (no shift to the left of the text on even pages). On the other hand, the creation of the \newgeometry for page type (in my case for backmatter) does not solve the problem of layout of the headers and footers which remain shifted because the value of marginparwidth used remains that of the document and not that defined in the new environment.
I think the problem may be related to using \geometry package implemented in the Tufte-book documentclass. Unlike in the \typearea package where it seems possible to adjust the position of headers and footers with headinclude or footinclude (headexclude and footexclude are default options), I don't find an equivalent procedure with \geometry.
I need help to fix it.