"Choose File Names" in "Load State Options" dialog not loading files in sequence

Download these files vtus.zip, unzip
Start ParaView, builtin server
Load the data files. There will be 4 time steps
File > Save State... Save the state somewhere.
Reset ParaView
Copy one of the .vtu files several times and rename the copied files to follow in the sequence (sphere0004.vtu, sphere0005.vtu, etc.) all in the same directories
Load the state file. In the Load State Options dialog, change the Load State Data File Options to "Choose File Names". Navigate to and choose the sphere000x.vtu sequence of files. Click OK, OK.

Only the initial 4 files will be loaded - none of the .vtu copies will be loaded.

To upload designs, you'll need to enable LFS and have an admin enable hashed storage. More information