The problem about the “automatically adjust resolution and bitrate” can be done in two ways:
Using a GPU to transcode the 4k video in real time (generally unavailable on VPS)
Encoding the video in multiple resolutions and bitrates, using much more disk space
Both solutions are expensive on a VPS.
In this case when I need to share stuff in 4k 60 (basically never) I just host on YouTube unlisted and having Google foot the bill. Maybe think like this: the content really deserves to be 4k 60 fps? Home videos that I share with my family are downgraded to 720p as anyway they will watch it horizontal on a vertical screen