How is this possible (I have no clue about FHE)? If the server can do operations on the image, then the image can't look like random noise, or not? And if there are indeed patterns the server can operate on, then the image can be decrypted?
FHE is precisely the magic that allows doing operations on encrypted data and get encrypted results that you can then decrypt to valid end result.
A blur or sharpen filter would be an easy example. The server sees you take the random noise of each pixel, mix it with the nearby pixels, and output new random noise.
Which means the pixel positions are known to the server, which means the image isn't really encrypted?
The server would know that you're doing a blur, but it would have no idea what the contents of the image are.
Your data is encrypted. Your program is not encrypted.
If you want to hide your program, then things will get much slower yet again.