ld.so and ldd don't use /etc/ld.so.conf to locate libraries. They use /etc/ld.so.cache, which is created by ldconfig from /etc/ld.so.conf. The cache is typically the first file opened by a dynamically linked binary.

# ls -la /usr/local/lib/libpython3.*
lrwxrwxrwx. 1 root root       19 Dec  9 16:49 /usr/local/lib/libpython3.8.so -> libpython3.8.so.1.0
-rwxr-xr-x. 1 root root 17356488 Dec  9 16:49 /usr/local/lib/libpython3.8.so.1.0
-rwxr-xr-x. 1 root root     7448 Dec  9 16:49 /usr/local/lib/libpython3.so
# ldd /usr/local/bin/python3.8
        linux-vdso.so.1 (0x00007fff499d9000)
        libpython3.8.so.1.0 => not found
        libc.so.6 => /lib/x86_64-linux-gnu/libc.so.6 (0x00007fd1cd2f9000)
        /lib64/ld-linux-x86-64.so.2 (0x00007fd1cd8ec000)
# ldconfig
# ldd /usr/local/bin/python3.8
        linux-vdso.so.1 (0x00007ffe19d9a000)
        libpython3.8.so.1.0 => /usr/local/lib/libpython3.8.so.1.0 (0x00007ff7f46f7000)
        libc.so.6 => /lib/x86_64-linux-gnu/libc.so.6 (0x00007ff7f4306000)
        libpthread.so.0 => /lib/x86_64-linux-gnu/libpthread.so.0 (0x00007ff7f40e7000)
        libdl.so.2 => /lib/x86_64-linux-gnu/libdl.so.2 (0x00007ff7f3ee3000)
        libutil.so.1 => /lib/x86_64-linux-gnu/libutil.so.1 (0x00007ff7f3ce0000)
        libm.so.6 => /lib/x86_64-linux-gnu/libm.so.6 (0x00007ff7f3942000)
        /lib64/ld-linux-x86-64.so.2 (0x00007ff7f4ea4000)