* lisp/emacs-lisp/syntax.el: Rework the handling of nested calls.

* lisp/emacs-lisp/syntax.el: Rework the handling of nested calls.

Nested calls to `syntax-ppss` and `syntax-propertize` can easily
happen unexpectedly via ondemand propertizing or `forward-sexp`.
Refine the handling of nested calls so we detect them more reliably
(e.g. also within `syntax-propertize-extend-region-functions`)
and so that the `syntax-ppss` cache is automatically flushed in case
it might have been filled with data that's become obsolete since.

(syntax-propertize--inhibit-flush): Delete var.
(syntax-propertize--in-process-p): New function to replace it.
(syntax-ppss-flush-cache): Use it.
(syntax-ppss--updated-cache): New var.
(syntax-propertize): Make `syntax-propertize--done` binding apply to
`syntax-propertize-extend-region-functions` as well, as intended (fixes
bug#46713).  Use `syntax-ppss--updated-cache` to flush
syntax-ppss cache at the end when needed.
Don't bind `syntax-propertize--inhibit-flush` any more.
(syntax-ppss): Set `syntax-ppss--updated-cache` when applicable.