Handle /LiveTv/Programs

[LLukas22]

A POST request to /LiveTv/Programs sends the following payload:

pub struct GetProgramsRequest {
    pub channel_ids: Option<Vec<String>>,
    pub user_id: Option<String>,
    pub genre_ids: Option<Vec<String>>,
    pub series_timer_id: Option<String>,
    pub library_series_id: Option<String>,

    #[serde(flatten)]
    pub extra: std::collections::HashMap<String, serde_json::Value>,
}

To handle this correctly, we’ll need to:

1. Filter the channel_ids field to figure out which server each ID belongs to.
2. Send a request to each server, including only the IDs that exist on that server.
3. Merge the results from all servers before returning them.