fix(72): report a real per-channel playout count on the channels API

The channels API could not answer "will this channel play?", which #72 needs
to flag a broken channel in the lineup at a glance.

Two defects, one root cause each:

1. `ChannelRepository.GetChannel` never included `Playouts`. The read is
   AsNoTracking with no lazy-loading proxies, so the navigation came back
   empty and `GetChannelByIdForApiHandler`'s `channel.Playouts?.Count ?? 0`
   could only ever evaluate to 0 — `GET /api/v1/channels/{id}` reported
   `playoutCount: 0` for every channel on the system. That silently disabled
   the channel editor's playout-source guard (ChannelEditScreen:820, gated on
   `playoutCount > 0`), so the "Cannot be changed once a generated channel has
   a playout" control was always live. The server still enforces the invariant
   (UpdateChannelHandler coerces Mirror back to Generated), so nothing was
   corrupted — but the user's change was silently discarded. That silent
   coercion is filed separately as #401.

2. The detail path counted only the channel's own playouts, never the mirror
   source's, so a working Mirror channel would read as "no playout" even once
   the include landed.

Both call sites now share `Mapper.GetPlayoutsCount` (previously private to
GetAllChannelsHandler), which handles the Mirror case. `ChannelResponseModel`
gains `PlayoutCount` so the list — #72's actual surface — can render it; the
count is free there, since `GetAll` already includes `Playouts` and
`MirrorSourceChannel.Playouts` and simply discarded them.

Tests run the real repository against a real context on purpose: a handler
test with a substituted IChannelRepository populates `Playouts` itself, so it
passes whether or not the query includes them. Proven non-vacuous — removing
the include again turns the 2-playout and mirror cases red (0 CS errors, so
no stale-dll false pass).

Refs #72

web/src/api/generated/v1.d.ts

@@ -239,6 +239,7 @@ export interface components {
     "streamingMode": string;
     "isEnabled": boolean;
     "showInEpg": boolean;
+    "playoutCount": number;
   };
     "ChannelSongVideoMode": "Default" | "WithProgress";
     "ChannelStateResponseModel": {