On Bandcamp, there’s a subscription feature which allows artists to exlclusively distribute music to subscribers.
https://bandcamp.com/subscriptions
eg: https://celer.bandcamp.com/subscribe
the exclusive releases seem not even be streamable.
There might be other subscriber features on other websites. Is there a way to reflect such exclusivity on Musicbrainz? Is an annotation enough or should the annotation field even be used for such a purpose?
Definitely, if it’s notable enough for you to want to add it as a release, use the disambiguation and annotation 
If you think it’s not notable enough to be a ‘official’ release, e.g. you would consider the ‘real’ album/EP/single release date to happen later, then you can also set it to type: promotional
There is little reason not to put any interesting bit of information you care about into annotations (the single exception being word-for-word copies of promotional texts, due to licensing).
In the context of bandcamp, I often use the annotation field to mention tracks that are included in the downloads, but hidden by the artists from the displayed tracklist for some reason.
I think they could be considered as promo releases (like the physical ones artists and labels distribute to various people in order to promote the upcoming release).
EDIT: I misread the original post, as far I understand those Bandcamp releases are targetted at fans, and there are no restriction on access (anyone can subscribe), so those are very normal releases to me.
If they were targetted at a restricted audience in the purpose to promote the album then to release through normal chanels, perhaps it’d be promo releases.
It all depends on the purpose.
i think there’s a difference between promotion and subscriber releases.
promotion is directed to the market in order to sell something
music available through subscriptions, on the other hand, is already sold.
now if artists send out subscription music to labels/magazines, that would be promotion.
“Promotion” has a really weird meaning here at MB.
If you PAY to be part of a fanclub, and you are sent special releases only available to those subscribers, then MB rules calls this a “promotion”.
This sounds the same as your Bandcamp Subscriptions example.
There really needs to be a “special subscriber only release” category. But as there isn’t, then MB says to make it a “promotion” if it is not available on the high street.
There is also a similar issue with Cover Mount discs with Magazines that they also are “promotional” even if it is the whole reason for the magazine to exist.
Many terms at MB don’t follow the English Dictionary Definition and cover some grey areas.