Paid for service, but not painfully priced, that will let you connect to remote RPi’s via the desktop without needing to configure the local router to allow incoming connections.
https://www.realvnc.com/en/raspberrypi/
Setup on the RPi
RealVNC Server is included with Raspberry Pi OS (formerly Raspbian). It’s completely free for non-commercial use; it just needs to be enabled:
Start > Preferences > Raspberry Pi Configuration > Interfaces > VNC = On
You should then get the RealVNC server icon in your bar next to the Bluetooth bar. Sign into your RealVNC account to add the RPi to it.
RPi5 – see below
Running on devices without a keyboard and mouse connected
You will need to install another entropy generator such as haveged, which you can install by running this command:
sudo apt install haveged
RPi5 issue late 2023
There’s an issue with RealVNC support for the default Raspberry Pi OS currently, to be resolved mid 2024 – details here.
You must be running the 64bit OS (shown on the startup splash screen).
First ensure that VNC is turned off in Start > Preferences > Raspberry Pi Configuration > Interfaces
On the command line run
raspi-config
Advanced Options > Wayland > Select X11 instead of the default Bookworm.
After your RPi reboots you will now be able to turn on VNC and see RealVNC run/appear.