Will writing to /dev/pts allow me to source ~/.bashrc?

I have several terminal windows already open; I just made a change to ~/.bashrc, and I'd like to run source ~/.bashrc in each of the open terminals. It seems to me that if I just

source ~/.bashrc | tee /dev/pts/{0..12}

, then ~/.bashrc should be run in each terminal. It looks like it was, since I include a clear at the end of ~/.bashrc. However, what I'm specifically testing is whether

PROMPT_COMMAND="history -a; history -c; history -r; ${PROMPT_COMMAND:+$PROMPT_COMMAND$'\n'}"

actually creates a single source of truth for all my terminals, and was modified in each open terminal. Now I'm not sure if this has something to do with writing to /dev/pts/{0..12} or is related to the way that history functions. If I look at one of my open terminals which is running git log, and echo $PROMPT_COMMAND, I do **NOT** see the modifications I would expect had ~/.bashrc been sourced. As a consequence of the history commands missing, I do not see git log output in a separate terminal, running tail -f ~/.bash_history, which I would expect to see if PROMPT_COMMAND was indeed modified after source ~/.bashrc. However, if I ask each terminal echo $PROMPT_COMMAND | tee /dev/pts/{0..12}, what the value of PROMPT_COMMAND is, I get:

history -a; history -c; history -r; pre_prompt_command; echo -ne "\033]0;${USER}@${HOSTNAME%%.*}:${PWD/#$HOME/\~}\007"

which includes history -a; history -c; history -r;, the changes that I added in ~/.bashrc. Now I'm confused. What am I doing wrong? Or what do I not understand correctly? Was PROMPT_COMMAND modified or was it not? Or is this a consequence of how bash / linux works? I'm pretty sure it's user error, and not a bug.