Does the docker container have gpu access for transcoding?

Not just an official act, it’s explicitly a constitutional power which is given absolute immunity.

Bone conduction earphones will let you listen to music without occluding external sound.

Starting with a consumer NAS is a good spot, they come with a lot of upfront features that are designed to be easier to use for someone who isn’t already familiar with them. I have a synology and it did all the things you describe without issue (other than struggling with transcoding video in real time) and eventually graduated the heavier tasks like media and proper VM hosting to external secondhand mini PCs while still using the NAS as a network drive to store the data. The NAS itself includes docker and an easy to use repository browser that I use for things like pinhole or WLAN controller software, it has an onboard torrent client (which can use RSS and regex to automate downloads), and it has some other light hosting services, which it’s quite capable of. Starting with “just” the NAS and adding external devices as your use case shifts is always an option. Keep in mind that the best way of upgrading a NAS’ storage is leaving a bay open and upgrading disks one by one without having it do a “hard” rebuild from parity data, so 4 bays at least is a good starting point.

If you want to start with just an off the shelf NAS as an all in one device I would recommend making sure it either has or can take additional RAM (no such thing as too much), an NVME cache (more optional but nice) and an intel processor (quicksync transcoding, though the low end cpus will definitely still struggle with trying to turn 4K into 1080 for a stream). I’d be willing to bet most of the consumer NAS devices will all support docker at this point and have similar built in feature sets. Some of the newer models will support onboard 2.5gbe which is nice but probably unnecessary for a single user or family.

External access would be more of a job for your router/firewall which would use PAT to forward connections to your internal network, so that’s outside the scope of your NAS unless you’re building a true all in one box that acts as the central hub of your entire home network.

“Simple” and “aesthetically pleasing” aren’t mutually exclusive!