Edit: thanks everyone for the suggestions. In the end I decided to buy a icy box usb3.1 4xhdd enclosure for around 100€. In the description it says it only works with mac and windows, but my Linux laptop works well with it, I guess the pi will to as well. I will print an enclosure for the power brick and the pi to screw to the drive case.
Here is why I choose this option: The pi is rather cheap compared to its power and also power consumption. I already had 4x4tb HDDs which I wanted to use, so at least 4 slots needed. The pi has 2x usb 3.0 connections which can be used simultaneously. One will be used for the 4bay, the other is free for now. I have the option to connect a second Nas case if I need more storage. Usb 3.0 is pretty fast, even if I don't get all the 5gbit/s. It's still faster than 1gbit/s ethernet.
I also thought about getting 2x 2xhdd enclosures to use the two usb3.0 at the same time. But decided against it because it would be a little more sketchy and I wanted to keep a free usb port for a second drive enclosure.
There are some enclosures that offer raid (hardware raid?) But I could not figure out if that would mean that all 4 drives will be raided, so I decided for the cheaper variant and would do the raid myself.
I plan on running 2 drives as raid1 and the other as raid 0 for secure storage and the other for movies and stuff I can download again.
Thanks again for all the comments!
It seems weirdly difficult to find a good solution to attach HDDs to my pi. Best case would be for me a enclosure with small power supply, space for my pi, and at least 2 bays for HDDs, rather 4. All that for under 100€ of cause :D
I could not really find cheap hhd enclosures that connect via usb. Any recommendations? I don't really want to use HDD toasters, they feel not permanent enough for a Nas. I could also not find sata to usb hats for the pi that are available right now
The Raspberry Pi would be a great low power device to have always on with some storage attached to backup to, store family photos, etc.
So not a high performance NAS, but good enough for this use case.
That is an understatement.
It entirely depends on what you want to do with it. So calling it underpowered is not a statement that can be made in general.
Disk I/O always been the weak point of RPi, with slow USB being the only way to attach drives, and the USB port sharing the same bus as the network controller. A requirement for a frequently used Network-Attached Storage is... well... decently fast network and storage access. The Pi will not cut it for this specific task (moving external USB drives around your house would be faster and more practical).
You not caring if it's underpowered doesn't mean it's not underpowered.
It depends if underpowered means "too slow" for you, or "slow". I would consider the meaning more similar to "too slow", i.e. I think the reference point matters. Therefore for me the pi is not underpowered, just low powered. [Edit: to keep the discussion on track, I would therefore consider the pi "good enough", which was the original claim in the second level comment]
Of course in terms of absolute numbers the pi has not a lot of processing power.