Why is the Linux command `unshare --pid=p --mount=m` not creating a persistent namespace?

From everything I have read in the unshare and nsenter man pages, I should be able to bind-mount a directory to itself, mount --make-private the directory, and then use files within that directory to hold refs for persistent namespaces. Here is what I'm doing, basically the same as the man unshare but with different directories and using --pid=file in addition to --mount=file # Terminal 1:

# mkdir -p /mnt/jails/debian/bookworm/.ns
# mount --bind /mnt/jails/debian/bookworm/.ns /mnt/jails/debian/bookworm/.ns
# touch /mnt/jails/debian/bookworm/.ns/{mount,pid}
# mount --make-private /mnt/jails/debian/bookworm/.ns
# unshare --fork --mount-proc --mount=/mnt/jails/debian/bookworm/.ns/mount --pid=/mnt/jails/debian/bookworm/.ns/pid /bin/sh & echo $!; fg
 151299
151299
sh-4.4# echo $$
1
sh-4.4# grep NS /proc/self/status
NStgid:	3
NSpid:	3
NSpgid:	3
NSsid:	0

So far so good, the container above is working. While that runs: # Terminal 2:

# nsenter  --mount=/mnt/jails/debian/bookworm/.ns/mount --pid=/mnt/jails/debian/bookworm/.ns/pid /bin/sh
sh-4.4# ps ax
Error, do this: mount -t proc proc /proc
# ls /proc/1/exe -l
lrwxrwxrwx. 1 root root 0 Jul 21 18:49 /proc/1/exe -> /usr/bin/bash
sh-4.4# mount -t proc proc /proc
sh-4.4# ps ax|head

sh-4.4# grep NS /proc/self/status
NStgid:	156987
NSpid:	156987
NSpgid:	156987
NSsid:	156921

I've also tried this in Terminal 2 (note the pid from Terminal 1) with the exact same results:

# nsenter -t 151299 -a  /bin/sh
sh-4.4# ps ax
Error, do this: mount -t proc proc /proc
# ls /proc/1/exe -l
lrwxrwxrwx. 1 root root 0 Jul 21 18:49 /proc/1/exe -> /usr/bin/bash
sh-4.4# mount -t proc proc /proc
sh-4.4# ps ax|head

sh-4.4# grep NS /proc/self/status
NStgid:	155356
NSpid:	155356
NSpgid:	155356
NSsid:	143538

For some reason nsenter is entering the host OS's pid space, however it does seem to see a the namespace of the correct /proc directory, but it is invalid for sh in terminal2 because the pid namespace isn't working so (I think) thats why ps ax gives an error. Also I've tried both with and without --mount-proc # Questions: How can I enter the PID namespace from Terminal 1? What am I doing wrong here? (Host linux kernel is 5.18 running Oracle Linux 8.)