According to Gary Brown (2001), floppy disks are called "floppy" because their packaging was a very flexible plastic envelope. These floppy disks were the very, very old ones from the 80's and 90's. The "modern" floppy disk of the 2000's Windows XP era, also known as the "diskette," were 3.5 inches and had a rigid case.
This means that by the time PCs got popular, floppy disks weren't "floppy" anymore, they were just called floppy.
For reference, here's a video about 8 inch floppies where you can see a bit of the floppiness of the floppies:
Quotes
The 5.25-inch disks were dubbed "floppy" because the diskette packaging was a very flexible plastic envelope, unlike the rigid case used to hold today's 3.5-inch diskettes.
Gary Brown "How Floppy Disk Drives Work" 26 February 2001 [https://computer.howstuffworks.com/floppy-disk-drive.htm] (accessed 2025-01-11)
Hello, today we're going to talk about floppies.
[Holds a rigid floppy disk and tries to bend it by the corners.]
Uh, not that floppy. It's not even floppy, so it doesn't count.
[Holds a five and a quarter inch floppy disk, waving it for the camera.]
But, the actual real floppy thing.
All you never wanted to know about 8 inch floppy drives [https://www.youtube.com/watch?v=oL0LXSE1jeM] (accessed 2025-01-11)