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