Hi Antoine,
and thanks for the good and well documented report.
I agree that for consistency doxygen search should work with the PHP
version we ship in any given
Debian release.
And this issue also applies to buster as it will ship doxygen 1.8.13 and
php 7.3.
Fixing it for buster is higher priority, and a solution could be to
backport doxygen 1.8.15,
but before that we need it in testing: https://bugs.debian.org/919413
Then for stretch, backporting it to stretch too is an option if it is
painless.
Another option is to just backport the upstream fix.
I propose that we keep this on hold for now.