Fix linting issues and finalize save-session implementation

Co-authored-by: pavelfeldman <883973+pavelfeldman@users.noreply.github.com>

README.md

@@ -164,6 +164,8 @@ Playwright MCP server supports following arguments. They can be provided in the
                                "http://myproxy:3128" or "socks5://myproxy:8080"
   --save-trace                 Whether to save the Playwright Trace of the
                                session into the output directory.
+  --save-session               Whether to save the session log with tool calls
+                               and snapshots into the output directory.
   --storage-state <path>       path to the storage state file for isolated
                                sessions.
   --user-agent <ua string>     specify user agent string

src/context.ts

@@ -52,9 +52,8 @@ export class Context {
     this.config = config;
     this._browserContextFactory = browserContextFactory;
     testDebug('create context');
-    if (this.config.saveSession) {
+    if (this.config.saveSession)
       void this._initializeSessionFile();
-    }
   }
 
   clientSupportsImages(): boolean {
@@ -163,9 +162,8 @@ export class Context {
     }
 
     // Add snapshot reference if provided
-    if (snapshotFile) {
+    if (snapshotFile)
       entry.push(`    snapshot: ${path.basename(snapshotFile)}`);
-    }
 
     entry.push(''); // Empty line for readability
 
@@ -214,9 +212,8 @@ export class Context {
     });
 
     // Log session entry if enabled
-    if (this.config.saveSession) {
+    if (this.config.saveSession)
       await this._logSessionEntry(tool.schema.name, params || {}, snapshotFile);
-    }
 
     const result: string[] = [];
     result.push(`### Ran Playwright code