It's actually not 4.0 RC1, but snapshot 200004141345.

apache version 1.3.12. 

Compiled with mod-so, works fine.

build and install of libphp4 without the --with-mysql works fine

config *with* --with-msyql=/web/mysql creates makefiles that seem to know
where things are.  For instance, my libphp4.la libtool line (from the output
of a "make" run) contains" -L/web/mysql/lib/mysql" and " -R /web/mysql/lib/mysql"

libmysqlclient.so does in fact exist in /web/mysql/lib/mysql

make and make install appear to run without complaint

Upon startup, or when doing a ldd -s, the mysql lib dir is not searched.  This
results in apache being unable to start.

Kludge temp workaround: set the env var LD_RUN_PATH in the shell which is doing
the compiling to /web/mysql/lib/mysql.  Then run make and make install.  This builds
a library for which ldd (or a runtime invocation via apache) does in fact look in the
mysql lib dir and finds my libmysqlclient.so