Add broadcast scheduling features: implement Show and Channel entities, enhance AppDbContext and DependencyInjection for broadcasting, and update API routing. Include migration for new database schema and update documentation for broadcast-related functionalities.

backend/src/TeleWave.Application/Library/RemoveEpisode/RemoveEpisodeCommand.cs

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+using LiteCqrs;
+using TeleWave.Application.Common.Models;
+
+namespace TeleWave.Application.Library.RemoveEpisode;
+
+public sealed record RemoveEpisodeCommand(Guid ShowId, Guid EpisodeId) : ICommand<Result>;

backend/src/TeleWave.Application/Library/RemoveEpisode/RemoveEpisodeCommandHandler.cs

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+using LiteCqrs;
+using Microsoft.EntityFrameworkCore;
+using TeleWave.Application.Common.Interfaces;
+using TeleWave.Application.Common.Models;
+
+namespace TeleWave.Application.Library.RemoveEpisode;
+
+public sealed class RemoveEpisodeCommandHandler(IAppDbContext dbContext)
+    : ICommandHandler<RemoveEpisodeCommand, Result>
+{
+    public async Task<Result> Handle(
+        RemoveEpisodeCommand command,
+        CancellationToken cancellationToken
+    )
+    {
+        var show = await dbContext.Shows
+            .Include(s => s.Episodes)
+            .FirstOrDefaultAsync(s => s.Id == command.ShowId, cancellationToken);
+        if (show is null)
+            return Result.Failure(ShowErrors.NotFound);
+
+        return show.RemoveEpisode(command.EpisodeId)
+            ? Result.Success()
+            : Result.Failure(ShowErrors.EpisodeNotFound);
+    }
+}