[The story or series is] to be continued [by the TV Channel]
The use of the passive here is crucial to meaning. Most native speakers would understand the verbal phrase as part of a full sentence not fully expressed.
This is not really an idiom.
The other variations mean something else and do not imply "by the TV Channel or producers or writers".
There are many instances where this structure would be used in a written situation (and often hand-written on a text or memo, etc.), for example:
to be done, to be finished, to be continued, to be reviewed.
In every instance, an agent and broader situation is implied:
For example:
[this work is] to be done [by John]
[this chapter is] to be finished [by you]
[this policy is] to be reviewed [by the committee].
So, the form to be + past participle is idiomatic but not an idiom.
