What if you try this instead?
diff --git a/configure.ac b/configure.ac
index bc7e61048c3..ac93d003b70 100644
--- a/configure.ac
+++ b/configure.ac
@@ -2806,6 +2806,25 @@ AC_DEFUN
WEBP_MODULE="libwebpdemux >= $WEBP_REQUIRED"
EMACS_CHECK_MODULES([WEBP], [$WEBP_MODULE])
+
+ # WebPGetInfo is sometimes not present inside libwebpdemux, so
+ # if it does not link, also check for libwebpdecoder.
+
+ OLD_CFLAGS=$CFLAGS
+ OLD_LIBS=$LIBS
+ CFLAGS="$CFLAGS $WEBP_CFLAGS"
+ LIBS="$LIBS $WEBP_LIBS"
+
+ AC_CHECK_FUNC([WebPGetInfo], [],
+ [WEBP_MODULE="$WEBP_MODULE libwebpdecoder >= $WEBP_REQUIRED"
+ HAVE_WEBP=no
+ AS_UNSET([WEBP_LIBS])
+ AS_UNSET([WEBP_CFLAGS])
+ EMACS_CHECK_MODULES([WEBP], [$WEBP_MODULE])])
+
+ CFLAGS=$OLD_CFLAGS
+ LIBS=$OLD_LIBS
+
AC_SUBST([WEBP_CFLAGS])
AC_SUBST([WEBP_LIBS])
fi
I'm not sure what pkg-config is doing here TBH, but it isn't very
intuitive.