nzb360 makes connections to web services with HTTP/1.1 even through proxies that support HTTP/2, as my nginx access log shows:

"GET /sabnzbd/api?mode=version&output=json&apikey=<redacted>&output=json HTTP/1.1" 200 20 "-" "-"

HTTP/2 has performance advantages which should improve speeds on remote connections especially.

Many nzb360 users run their services through a reverse proxy like nginx which has supported HTTP/2 for years.

SABmini on iOS, the closest competitor to nzb360 (for SABnzbd at least), does support HTTP/2 as shown below:

"GET /sabnzbd/api?apikey=<redacted>&ma_username=&ma_password=&output=json&mode=version HTTP/2.0" 200 40 "-" "SABmini/388 CFNetwork/976 Darwin/18.2.0"