I have not setup these particular XDG variables, but i have been able to use bash without creating any files in my home dir (i was also able to use firefox (librewolf) without having .dir in my $HOME)

first I do not use bash as my default shell (I am on arch and installed dash and a package which basically symlinks /bin/sh to dash (I think i it is called dashbinsh), because it is slightly faster (I have many shell scripts, for some of them difference is perceivable) and it does not create any files by default

also I use a login display manager (ly) (if you use something else, then that does not really change anything, if you just type out the command in tty, just the command will change), and I have edited my sway desktop file (/usr/share/wayland-sessions/sway.desktop), you can use any other de/wm, just replace the specific command to launch sway (here sway), with something else (for example, in xfce (a de), you have start-xfce4 command), and the desktop file used

[Desktop Entry]
Name=Sway
Comment=An i3-compatible Wayland compositor
Exec=sway-wrapper
Type=Application

I made a script sway-wrapper, placed it at /home/sg/.local/bin/sway-wrapper (my user name here is sg), and symlinked it to /bin/sway-wrapper

these are the only changes made to root system

here is my full sway-wrapper, it launches sway, and also declares all my system variables

#!/bin/sh
# here i have exported many variables, not necessary for now
# export A_LOT_OF_THINGS
exec sway

now I use bash as my shell (I also tried zsh, but was not really amazed), and I only use it in my terminal emulator (if you use it elsewhere (if in editors, most have some way to set the shell used, if in tty, then I think you can set via some systemd init thing that I have forgotten, but most likely you would not have to set it at many places), so I edited my terminal emulator's (foot) config file to launch with bash, but with a specific rc file,

shell=bash --rcfile /home/sg/.local/bin/bashrc.sh

(most terminal emulators have some way to set this)

and in my bashrc, i have

# many things, this is just your bashrc, you can simply move your old one here with almost no changes (if you pull some variables/aliases with relative path, then change them)
export HISTFILE=${XDG_DATA_HOME}/bash-history

and also do

touch ${XDG_DATA_HOME}/bash-history

beforehand, as bash does not create hist file if it does not already exist

I also started using different programs or use hem with different cli flags (with help of launch scripts) to have there stuff in different directories

Outside of xdg specification dirs, I have .librewolf (if you want to not have this(this approach works with pretty much all firefox derivatives/family), then make a script, which basically launches librewolf with different home, like HOME=$XDG_DATA_HOME librewolf (or wherever you want), after doing so, you may have to reinstall extensions, but they do not lose there data, also maybe have to reset the download path, or if you use nativemessaging (some extensions use this), you may hae to slightly edit them, then either create a different desktop file to launch browser with this script, or edit the existing desktop file for your browser(with first approach you would have to reset your default browser everywhere (either by choosing it again, or editing your mime file in .config), with the latter approach, you may have to edit your desktop file after each browser update))(i stopped doing because i have some broken mime issue that pretty much every file type that i have not already set the default opener for, got opened with browser, and that created the .dot dir again and again), and some proprietary stuff that i have tried with the browser approach, and it still does not work