I've been occasionally using Microsoft's RDP Client [0] on my iPhone with external keyboard + mouse with a usb-c cable into my external monitor (with a Logitech RF dongle connected to the back of it).
It worked okay, the mouse support is somewhat of a hack, but keyboard works awesome.
The biggest annoyance was actually getting RDP to work satisfactory on a linux box with no external monitor plugged in to it (hetzner box).
I thought someone would have created an app to run browser on the external screen in full resolution, so I could skip RDP and use vscode server via the browser. But the only option seems to be infinitex2p which is not available in the EU :(.
[0]: Which in typical Microsoft idiotic fashion semi recently got renamed to "Windows app"... [1]: https://x.com/infinitex2p
I've run vscode over ssh via tailscale before and it was pretty good, I'm mostly connecting to a remote using rustdesk however, that also requires a "dummy" hdmi to operate. The only thing it needs to make it perfect would be if there were officially supported forwarded web browsing windows in vscode. I wish apple would actually let us use "our" usb-c as.. usb-c