I have been able to use the macOS version of Affinity Photo's Astrophotography Stack to open FITS files directly from the ASIAIR's USB (or microSD card) after mounting the ASIAIR Samba server on my macOS Desktop.
I do not even have to make a copy of the file on the Mac's own file system -- just grab it directly from the ASIAIR's storage into the Affinity Photo application.
However, being able to send a FITS file over to the iPad may not solve your problem.
Since the Astrophotography Persona only exists on the macOS version of Affinity Photo for now, the iPad version of Affinity Photo will not (yet) open FITS files for me.
I could copy PNG files from the Mac over to the iPad and let Affinity Photo stack them. But not FITS files.
On macOS, Affinity Photo shows both a "New Stack..." (which does not open FITS) and a "New Astrophotography Stack..." in the File Menu.
But the iPad version (that I have) only shows "New Stack" (which also does not open FITS files) and no "New Astrophotography Stack".
For now, you will need to convert FITS to PNG or TIFF, before sending it over to the iPad.
Chen