Link handler to automatically choose the correct browser based on the link. Set as your default link handler.

link-handler.sh

#!/usr/bin/env bash

shopt -s nocasematch

# Links to use special browser for
if [[ "$1" =~ "github.com/my-org" ]] ||
   [[ "$1" =~ "my-org.atlassian.net" ]] ||
   [[ "$1" =~ "auth.atlassian.com" ]] ||
   [[ "$1" =~ "my-org" ]] ||
   [[ "$1" =~ "https://localhost:4321" ]]; then
  # Special browser
  gtk-launch firefox-my-org.desktop $1
else
  # Default browser
  gtk-launch firefox-personal.desktop $1
fi