Does anyone know of an option to use remote control of the radio without having to connect / log in to a third party system? I do not like to "give control" of my devices to others, not even the vendors.
This was probably possible on ESDR2, but I'm looking for an alternative to ESDR3.

The website at cloud.eesdr.com:5450 looks relatively simple, and it should be possible for Expert Electronics to create a version of this that you can download and run on your own server.
Maybe someone from Expert Electronics can also answer this?

Cloud.eesdr.com:5450

Is nothing more than a secure authentication connection handshake

One you have authenticated using the above site that is all that takes place,
After the security is checked and handshake is approved: Your remote connection to wherever your rig is located is a Direct 1:1 connection, cloud.eesdr.com:5450 site is no longer part of the routing. it is just a secure way and handshake of checking you are who you say you are.

If you do not like using that then your choices are one of many Remote connection options such as: TeamViewer, VNC, Splashtop etc. but recall using these methods add another application on each end that will also utilize part of your available bandwidth and you may get less performance in doing so- you will also need to route your input and output audio between the two using these methods as well.

Again the cloud.eesdr.com site is nothing more than an authentication server and once authenticated the connection is direct between the remote and the site where your rig is located

Another way you can try is by extending the local area network using VPN. This allows your remote client to appear on the network where the radio is on as if it was on the same network. This can work well (it is what I'm using) but the current EESDR3 build tends to disconnect if the latency is too high (above 5ms). What you need is to have a VPN client and host.