Update LlmService to prioritize Gemini as the default provider for BYOK and adjust provider selection logic

- Changed the default LLM provider for BYOK from Claude to Gemini.
- Updated the provider selection priority to Gemini > OpenAI > Claude for improved service efficiency.
- Removed redundant gemini provider check from the SelectProvider method to streamline the logic.

src/Managing.Application/LLM/LlmService.cs

@@ -74,7 +74,7 @@ public class LlmService : ILlmService
         // BYOK: If user provides their own API key
         if (!string.IsNullOrWhiteSpace(request.ApiKey))
         {
-            var requestedProvider = ParseProviderString(request.Provider) ?? LlmProvider.Claude; // Default to Claude for BYOK
+            var requestedProvider = ParseProviderString(request.Provider) ?? LlmProvider.Gemini; // Default to Gemini for BYOK
             var providerName = ConvertLlmProviderToString(requestedProvider);
             provider = CreateProviderWithCustomKey(requestedProvider, request.ApiKey);
             _logger.LogInformation("Using BYOK for provider: {Provider} for user: {UserId}", providerName, user.Id);
@@ -143,7 +143,11 @@ public class LlmService : ILlmService
 
     private ILlmProvider SelectProvider()
     {
-        // Priority: OpenAI > Claude > Gemini
+        // Priority: Gemini > OpenAI > Claude
+        var geminiKey = ConvertLlmProviderToString(LlmProvider.Gemini);
+        if (_providers.TryGetValue(geminiKey, out var gemini))
+            return gemini;
+        
         var openaiKey = ConvertLlmProviderToString(LlmProvider.OpenAI);
         if (_providers.TryGetValue(openaiKey, out var openai))
             return openai;
@@ -152,10 +156,6 @@ public class LlmService : ILlmService
         if (_providers.TryGetValue(claudeKey, out var claude))
             return claude;
 
-        var geminiKey = ConvertLlmProviderToString(LlmProvider.Gemini);
-        if (_providers.TryGetValue(geminiKey, out var gemini))
-            return gemini;
-
         throw new InvalidOperationException("No LLM providers are configured. Please add API keys to configuration.");
     }