Background: our server supports both HTTP/2 and HTTP/1.1 protocols.
However, during tests, it appeared that HTTP/1.1 is much faster for files upload
No this is not possible. HTTP/2 is a connection level setting that is negotiated by the browser as part of the HTTPS set up and cannot be overridden for certain AJAX calls nor set for particular paths.
The only way this would be possible would be to host this on a separate domain with a separate HTTPS certificate.