I am not sure the best place to post this, but my testing suggests that using the save method for templates (or at least FastGridTemplate) does not write the contents of pn.config.raw_css to the requested html file. I first reported this 29 days ago when I thought it was a tabulator thing [https://discourse.holoviz.org/t/tabulator-not-including-css-in-save-html-files/2848], but I believe it is a missing from the panel .save method.
Let me know if there is a better place to report/request this bug/fix.