Restructured the project structure back to the way it was, there's no reasonable way to split the modules

src/NadekoBot/Modules/Searches/Search/Youtube/IYoutubeSearchService.cs

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+namespace NadekoBot.Modules.Searches.Youtube;
+
+public interface IYoutubeSearchService
+{
+    Task<VideoInfo?> SearchAsync(string query);
+}

src/NadekoBot/Modules/Searches/Search/Youtube/InvidiousSearchResponse.cs

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+using System.Text.Json.Serialization;
+
+namespace NadekoBot.Modules.Searches;
+
+public sealed class InvidiousSearchResponse
+{
+    [JsonPropertyName("videoId")]
+    public string VideoId { get; set; } = null!;
+}

src/NadekoBot/Modules/Searches/Search/Youtube/InvidiousYtSearchService.cs

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+using NadekoBot.Modules.Searches.Youtube;
+using System.Net.Http.Json;
+
+namespace NadekoBot.Modules.Searches;
+
+public sealed class InvidiousYtSearchService : IYoutubeSearchService, INService
+{
+    private readonly IHttpClientFactory _http;
+    private readonly SearchesConfigService _scs;
+    private readonly NadekoRandom _rng;
+
+    public InvidiousYtSearchService(
+        IHttpClientFactory http,
+        SearchesConfigService scs)
+    {
+        _http = http;
+        _scs = scs;
+        _rng = new();
+    }
+
+    public async Task<VideoInfo?> SearchAsync(string query)
+    {
+        ArgumentNullException.ThrowIfNull(query);
+
+        var instances = _scs.Data.InvidiousInstances;
+        if (instances is null or { Count: 0 })
+        {
+            Log.Warning("Attempted to use Invidious as the .youtube provider but there are no 'invidiousInstances' "
+                        + "specified in `data/searches.yml`");
+            return null;
+        }
+
+        var instance = instances[_rng.Next(0, instances.Count)];
+
+        using var http = _http.CreateClient();
+        var res = await http.GetFromJsonAsync<List<InvidiousSearchResponse>>(
+            $"{instance}/api/v1/search"
+            + $"?q={query}"
+            + $"&type=video");
+
+        if (res is null or {Count: 0})
+            return null;
+
+        return new VideoInfo(res[0].VideoId);
+    }
+}

src/NadekoBot/Modules/Searches/Search/Youtube/VideoInfo.cs

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+namespace NadekoBot.Modules.Searches.Youtube;
+
+public readonly struct VideoInfo
+{
+    public VideoInfo(string videoId)
+        => Url = $"https://youtube.com/watch?v={videoId}";
+
+    public string Url { get; init; }
+}

src/NadekoBot/Modules/Searches/Search/Youtube/YoutubeDataApiSearchService.cs

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+namespace NadekoBot.Modules.Searches.Youtube;
+
+public sealed class YoutubeDataApiSearchService : IYoutubeSearchService, INService
+{
+    private readonly IGoogleApiService _gapi;
+
+    public YoutubeDataApiSearchService(IGoogleApiService gapi)
+    {
+        _gapi = gapi;
+    }
+
+    public async Task<VideoInfo?> SearchAsync(string query)
+    {
+        ArgumentNullException.ThrowIfNull(query);
+
+        var results = await _gapi.GetVideoLinksByKeywordAsync(query);
+        var first = results.FirstOrDefault();
+        if (first is null)
+            return null;
+
+        return new()
+        {
+            Url = first
+        };
+    }
+}

src/NadekoBot/Modules/Searches/Search/Youtube/YtdlYoutubeSearchService.cs

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+namespace NadekoBot.Modules.Searches.Youtube;
+
+public sealed class YtdlYoutubeSearchService : YoutubedlxServiceBase, INService
+{
+    public override async Task<VideoInfo?> SearchAsync(string query)
+        => await InternalGetInfoAsync(query, false);
+}

src/NadekoBot/Modules/Searches/Search/Youtube/YtdlpYoutubeSearchService.cs

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+namespace NadekoBot.Modules.Searches.Youtube;
+
+public sealed class YtdlpYoutubeSearchService : YoutubedlxServiceBase, INService
+{
+    public override async Task<VideoInfo?> SearchAsync(string query)
+        => await InternalGetInfoAsync(query, true);
+}

src/NadekoBot/Modules/Searches/Search/Youtube/YtdlxServiceBase.cs

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+namespace NadekoBot.Modules.Searches.Youtube;
+
+public abstract class YoutubedlxServiceBase : IYoutubeSearchService
+{
+    private YtdlOperation CreateYtdlOp(bool isYtDlp)
+        => new YtdlOperation("-4 "
+                             + "--geo-bypass "
+                             + "--encoding UTF8 "
+                             + "--get-id "
+                             + "--no-check-certificate "
+                             + "--default-search "
+                             + "\"ytsearch:\" -- \"{0}\"",
+            isYtDlp: isYtDlp);
+
+    protected async Task<VideoInfo?> InternalGetInfoAsync(string query, bool isYtDlp)
+    {
+        var op = CreateYtdlOp(isYtDlp);
+        var data = await op.GetDataAsync(query);
+        var items = data?.Split('\n');
+        if (items is null or { Length: 0 })
+            return null;
+
+        var id = items.FirstOrDefault(x => x.Length is > 5 and < 15);
+        if (id is null)
+            return null;
+
+        return new VideoInfo()
+        {
+            Url = $"https://youtube.com/watch?v={id}"
+        };
+    }
+
+    public abstract Task<VideoInfo?> SearchAsync(string query);
+}