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/Broadcast/CreateOverride/CreateProgrammingOverrideCommand.cs

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+using LiteCqrs;
+using TeleWave.Application.Common.Models;
+using TeleWave.Domain.Broadcast;
+
+namespace TeleWave.Application.Broadcast.CreateOverride;
+
+public sealed record CreateProgrammingOverrideCommand(
+    Guid ChannelId,
+    OverrideMode Mode,
+    DateTimeOffset StartsAtUtc,
+    DateTimeOffset EndsAtUtc,
+    IReadOnlyList<OverrideShowInput> Shows
+) : ICommand<Result<Guid>>;

backend/src/TeleWave.Application/Broadcast/CreateOverride/CreateProgrammingOverrideCommandHandler.cs

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+using LiteCqrs;
+using Microsoft.EntityFrameworkCore;
+using TeleWave.Application.Common.Interfaces;
+using TeleWave.Application.Common.Models;
+
+namespace TeleWave.Application.Broadcast.CreateOverride;
+
+public sealed class CreateProgrammingOverrideCommandHandler(IAppDbContext dbContext)
+    : ICommandHandler<CreateProgrammingOverrideCommand, Result<Guid>>
+{
+    public async Task<Result<Guid>> Handle(
+        CreateProgrammingOverrideCommand command,
+        CancellationToken cancellationToken
+    )
+    {
+        if (command.EndsAtUtc <= command.StartsAtUtc)
+            return Result.Failure<Guid>(ChannelErrors.InvalidOverrideWindow);
+        if (command.Shows.Count == 0)
+            return Result.Failure<Guid>(ChannelErrors.OverrideNeedsShow);
+
+        var channel = await dbContext.Channels
+            .Include(c => c.Overrides)
+            .ThenInclude(o => o.Shows)
+            .FirstOrDefaultAsync(c => c.Id == command.ChannelId, cancellationToken);
+        if (channel is null)
+            return Result.Failure<Guid>(ChannelErrors.NotFound);
+
+        var showIds = command.Shows.Select(s => s.ShowId).Distinct().ToList();
+        var existingCount = await dbContext.Shows.CountAsync(
+            s => showIds.Contains(s.Id),
+            cancellationToken
+        );
+        if (existingCount != showIds.Count)
+            return Result.Failure<Guid>(ChannelErrors.ShowNotFound);
+
+        var ovr = channel.AddOverride(command.Mode, command.StartsAtUtc, command.EndsAtUtc);
+        foreach (var show in command.Shows)
+            ovr.AddShow(show.ShowId, show.Weight);
+
+        return Result.Success(ovr.Id);
+    }
+}

backend/src/TeleWave.Application/Broadcast/CreateOverride/CreateProgrammingOverrideCommandValidator.cs

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+using FluentValidation;
+
+namespace TeleWave.Application.Broadcast.CreateOverride;
+
+public sealed class CreateProgrammingOverrideCommandValidator
+    : AbstractValidator<CreateProgrammingOverrideCommand>
+{
+    public CreateProgrammingOverrideCommandValidator()
+    {
+        RuleFor(x => x.Shows).NotEmpty();
+        RuleForEach(x => x.Shows).ChildRules(s => s.RuleFor(i => i.Weight).InclusiveBetween(1, 1000));
+    }
+}

backend/src/TeleWave.Application/Broadcast/CreateOverride/OverrideShowInput.cs

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+namespace TeleWave.Application.Broadcast.CreateOverride;
+
+public sealed record OverrideShowInput(Guid ShowId, int Weight);