I’m not sure there’s some confusion of what is being controlled and where.
The HA’s (most modern digital ones) have buttons that can control volume and programs on the HA’s.
A streamer is required for many HA’s to allow outside sources to “pipe” into the HA’s and perhaps also in addition to the HA’s themselves to control programs and volume. These sources could be a phone, a music player, a tv etc. Most of these streamers offer wireless connectivity to those devices that can output wirelessly.
Several HA’s can wirelessly connect directly to a device without a streamer ie. iphone and one HA to Android. I assume they would simply use the built-in volume control but not sure about programs. But then they would need to be “connected” to be useful.
And another thing is app control from a smartphone. These can also control volume and program choices.
I’ve made several edits. This is 13:19PST