improve the language and logging guide

Author: amirejaz

docs/toolhive/guides-cli/manage-mcp-servers.md

@@ -30,7 +30,9 @@ thv list --all
 
 ### View server logs
 
-To view the logs of a running or stopped MCP server, use the
+#### Containerized servers
+
+To view the logs of a running or stopped containerized MCP server, use the
 [`thv logs`](../reference/cli/thv_logs.md) command. You can optionally follow
 the logs with the `--follow` option, which shows the most recent log entries and
 updates in real time.
@@ -39,8 +41,11 @@ updates in real time.
 thv logs <SERVER_NAME> [--follow]
 ```
 
-Logs are stored in the ToolHive application directory. The path depends on your
-platform:
+#### Remote servers
+
+The thv logs command only works with local containers. For remote MCP servers,
+there’s no container to read logs from, so you’ll need to check the log files
+directly in the ToolHive application directory. The path depends on your platform:
 
 - **macOS**: `~/Library/Application Support/toolhive/logs/<SERVER_NAME>.log`
 - **Linux**: `~/.local/share/toolhive/logs/<SERVER_NAME>.log`

docs/toolhive/guides-cli/run-mcp-servers.mdx

@@ -33,7 +33,7 @@ thv run fetch
 ### Remote MCP servers
 
 Remote MCP servers in the registry don't run as local containers but instead use
-ToolHive's transparent http proxy to forward requests to remote servers. For
+ToolHive's transparent HTTP proxy to forward requests to remote servers. For
 example:
 
 ```bash
@@ -61,6 +61,8 @@ To run a remote notion mcp server, you should use the `notion-remote` name.
 thv run notion-remote
 ```
 
+Use `thv search <NAME>` or `thv registry list` to discover available servers.
+
 :::
 
 :::info[What's happening?]
@@ -657,20 +659,21 @@ registration, eliminating the need to pre-configure client ID and secret.
 
 #### OIDC authentication
 
-For servers using OpenID Connect (OIDC), you can provide the issuer URL:
+For servers using OpenID Connect (OIDC), provide the issuer URL, client ID, and
+client secret obtained from the application provider:
 
 ```bash
 thv run https://api.example.com/mcp \
   --name my-server \
   --remote-auth-issuer https://auth.example.com \
-  --remote-auth-client-id my-client-id
+  --remote-auth-client-id my-client-id \
   --remote-auth-client-secret my-client-secret
 ```
 
 #### OAuth2 authentication
 
-For servers using OAuth2, you can specify the authorization and token URLs
-manually:
+For servers using OAuth2, specify the authorization and token URLs along with
+the client ID and secret obtained from the application provider:
 
 ```bash
 thv run https://api.example.com/mcp \
@@ -855,11 +858,7 @@ If a server crashes or exits unexpectedly:
 
 If a remote MCP server authentication fails:
 
-1. Check the server logs for authentication errors:
-
-   ```bash
-   thv logs <SERVER_NAME>
-   ```
+1. Check the server logs for authentication errors (see [View server logs](./manage-mcp-servers.md#view-server-logs) for the correct log file path on your platform)
 
 2. Verify the issuer URL is correct and accessible