Xbox One hdd spends a lot of time doing "nothing" after switching on.

I guess you mean for the powering on issue.

No I don't and the laptop is usually on battery and gets charged on a separate outlet, also the Xbox was on wired ethernet and the laptop on wi-fi.

I used to always shut the Xbox down into energy saver mode but it would sometimes switch on by itself when I would boot my laptop which uses the same Microsoft account. I don't run any of the xbox apps at startup except the gamebar which is "built in".

Since doing the full shutdown the xbox has not started by itself.

So basically the Xbox is doing stuff for 20-30 minutes, I guess indexing the drives to see if I have added any media, checking things etc and then it stops and nothing after that for the rest of the time the box is on doing nothing or in standby mode until I switch it off with a full shutdown and switch it on again and this 20-30 minute process starts again.

I understand that, it just that 20-30 minutes did seem a rather long time.

As a side note, the reason for the full shutdowns is this.

All my games but no media are on the external drive.

The point is I am not actually using the console, there are no downloads / updates happening the controller is off but the disk is still making noises for over 20 minutes.

I could understand if for example manually checking for updates only checked the last few games played and letting the console sit there means it checks my whole library but it would be nice to know what is actually happening.

It is a 4TB drive with about 3TB used consisting nearly exclusively of Game Pass and Gold games.

Even when you are not doing nothing the external storage will be read by the console, this is how external storage works, it's part of having the content available for use on the console

You have a controller plugged on the Laptop? It's the laptop using the same power outlet?