My home server’s case is the Fractal Design Meshify 2 and it has 14 3.5”/2.5” slots in the “Storage” configuration. It supports 6 in the default case configuration. There are also a couple 2.5” slots. I recommend the case and I’m considering getting another for my gaming PC, since I want it to support more HDDs than its current case can handle.
There are a couple variants of the Meshify 2. The RGB seems identical storage capacity-wise. The XL variant has 4 more 3.5”/2.5” slots when in the Storage configuration (18 total). The smaller variants don’t have enough slots for your needs.
In the Storage configuration, the slots in the storage bay (8 for regular, 12 for XL) are individually accessible and a single one can be pulled at a time if you just pull out the cables and unscrew a single screw - not quite a hot swap, but for me close enough. For an occasional troubleshooting or expansion of storage, this is more than convenient enough.
That all said, this is a traditional form factor tower, not something that would fit in a server rack.