How to update Bash custom prompt to display git status and refresh after file and folder changes?

I added to the ~/.bashrc a PS1 with changes to the bash prompt so it also shows git branches and status, but if i'm in not a folder with git and goes to one in the terminal, it won't run that PS1 ( because when I opened the terminal it wasn't on a git folder )

Same goes to when i'm in a git folder ( showing the branche and status ), if I make changes or commits it doesn't change the status of git in it.

This is the relevant code from my .bashrc.

tput sgr0;
reset=$(tput sgr0);
white=$(tput setaf 15);
violet=$(tput setaf 61);
green=$(tput setaf 64);
purple=$(tput setaf 125);
yellow=$(tput setaf 136);

prompt_git() {
	local s='';
	local branchName='';

	# Check if the current directory is in a Git repository.
	git rev-parse --is-inside-work-tree &>/dev/null || return;

	# Check for what branch we’re on.
	# Get the short symbolic ref. If HEAD isn’t a symbolic ref, get a
	# tracking remote branch or tag. Otherwise, get the
	# short SHA for the latest commit, or give up.
	branchName="$(git symbolic-ref --quiet --short HEAD 2> /dev/null || \
		git describe --all --exact-match HEAD 2> /dev/null || \
		git rev-parse --short HEAD 2> /dev/null || \
		echo '(unknown)')";

	# Check for uncommitted changes in the index.
	if ! $(git diff --quiet --ignore-submodules --cached); then
		s+='+';
	# Check for unstaged changes.
	elif ! $(git diff-files --quiet --ignore-submodules --); then
		s+='!';
	# Check for untracked files.
	elif [ -n "$(git ls-files --others --exclude-standard)" ]; then
		s+='?';
	# Check for stashed files.
	elif $(git rev-parse --verify refs/stash &>/dev/null); then
		s+='$';
	else
		s+='-';
	fi;

	echo -e "\[${white}\] on \[${violet}\]${branchName} \[${purple}\][${s}]";
}

PS1="\[\033]0;\W\007\]";
PS1+="\[${green}\]\w";

PS1+="$(prompt_git)";

PS1+="\[${white}\]: $ \[${reset}\]";
export PS1;

PS2="\[${yellow}\]→ \[${reset}\]";
export PS2;

I would like to know if there is a way to "refresh" the PS1 when there is folder changes, git commands and if possible file changes to update the status and branches.

So after reading about bash strings it looks like double quotes get evaluated before its saved, and single ones evaluate later.

So with that in mind I changed to this and it works:

# prompt_git
echo -e "${violet}${branchName} ${purple}[${s}]";

# after
PS1+="\[${white}\] on ";
PS1+='$(prompt_git)';

But still would be cool if file changes could also change the status itself.