As a decade(s)-long fan of Panics Transmit desktop version after trying most other file xfer/remote storage software.
The iOS UI is simple enough for me. To help the first reviewer with the issue of having to send a single file at a time, save or save as your files ("Open in...”) into ZipPro or an equivalent so you can compress them into a single file (within reason, of course; a 2TB .psb file for example is pushing it, although Ive found that "wrapping largecompressing single large image files into a an protect the file from corruption during transmission).
barnettart about Transmit