If you enable ssh on the Pi4, and install the desired browser you can cause the browser to run on the Pi and display on another system via XWindows without installing a desktop environment on your Pi.
You'll need to have an XServer installed on the other system (your Windows, Linux, Mac, etc desktop system). On Windows there are choices such as Xming, cygwin, or vcxsrv.
Once you have it all set up, you can remotely start the browser from your Windows/Linux/Mac system via ssh and direct it to display on the Xserver.
Here's one way:
On Windows: I use cygwin, and install the Xserver (packages xauth, xhost, xlaunch, xload, xorg-docs, xorg-scripts, xorg-server, xrdb, xset, xterm). I also install keychain for ssh key management.
In my .XWinrc file on the Windows system I have lines similar to the following:
"pisrv1 xterm" exec "/home/bls/bin/fullstartapp pisrv1.starwhite.net xterm"
fullstartup contains:
#!/bin/bash
# keychain must have already been run
#keychain -q --nogui --agents ssh id_dsa
source /home/<youruseridhere>/.keychain/$(hostname)-sh
exec ssh -Xn $*
You can read about ssh keys and keychain at Arch Linux SSH keys or Guide to setting up SSH
On the Pi, do:
apt install chromium-browser firefox-esr xauth xfonts-base xfonts-75dpi xfonts-scalable
This is not 100% complete, but will get you going down the right path, and happy to provide clarifications or further guidance.
