There's drag and drop support in streamtuner2 since 2.1.7, primarily meant for exporting individual stations into .XSPF or .PLS files, or dragging them into audio players.

There is also support for proper XDND payloads. However most BSD/Linux desktop applications support little more than STRING or text/uri-list file dragging. There's no standardization in or beyond that. Which is because nobody bothers to document anything. So as exception to the rule:

drag target MIME type	info id	content / payload	actions
audio/x-mpegurl	20	#EXTM3U #EXTINF;-1,Title http://example.org/stream.mp3 …	DEFAULT+COPY
application/x-scpls	21	[Playlist] File1=http://example.org/stream.mp3 Title1=Radio …	DEFAULT+COPY
application/xspf+xml	22	<playlist xmlns=…> <track><title>Radio</title> <location>http://example.org/stream.mp3</location> …	DEFAULT+COPY
application/smil text/html	23	<seq> <audio src="http://example.org/stream.mp3"> …	DEFAULT+COPY
application/jspf+json	25	{ "playlist": { "track":{ "location": "http://example.org/stream.mp3" …	DEFAULT+COPY
application/x-desktop	26	[Desktop Entry] Type=Link URL=http://example.org/stream.mp3 Title=Radio …	DEFAULT+COPY
text/url message/external-body	27	[InternetShortcut] URL=http://example.org/stream.mp3	DEFAULT+COPY
url/direct text/iri-list	15	http://example.org/stream.mp3	DEFAULT+COPY
FILE_NAME	3	/tmp/streamtuner2/RadioStation.pls	DEFAULT+COPY
text/uri-list	4	file:///tmp/streamtuner2/RadioStation.xspf	DEFAULT+COPY
TEXT STRING UTF8_STRING text/plain	5	http://example.org:8309/listen.pls # Title: Radio # Description: Current song etc..	DEFAULT+COPY
json/vnd.streamtuner2.station (internal JSON format)	51	[  {   "url": "http://example.org:8429/.ogg",   "title": "Radio station name"  }, …	SAMEAPP+ACTIONMOVE

<style> .content table td { border-bottom: 3px dashed #ddd; } .content table td { font-size: 80%; } </style>

• The example payloads are abstracted here.
• The info ids are just Gtk-internal.
• Ordering doesn't reflect priority handling.

As said, only text/uri-list is used in practice. It doesn't allow actual streaming URLs being transferred. Instead streamtuner2 has to create temporary export files. And since this dumb approach doesn't allow any content-negotation, a preconfigured default playlist format will be used for temp files. (Defaults to XSPF for crashing Rhythmbox.)

Alternatively there's text/iri-list now (yes, why not go with the century?) and url/direct to get a direct streaming URL/IRL.