LibWeb: Update the stored textarea value upon change

And fire the "input" event upon change. This is needed to submit a
comment on GitHub; otherwise, GitHub thinks the textarea value is empty.

Tests/LibWeb/Text/expected/textarea-value.txt

@@ -2,3 +2,4 @@
 2. "PASS"
 3. "PASS"
 4. 4
+5. "PASS"

Tests/LibWeb/Text/input/textarea-value.html

@@ -35,5 +35,19 @@
             textarea.innerHTML = 'PASS';
             return textarea.textLength;
         });
+
+        // 5. Textarea input via keyboard events.
+        testPart(() => {
+            const textarea = document.createElement('textarea');
+
+            // The element currently has to be part of a document to be able to receive keyboard events.
+            document.body.appendChild(textarea);
+
+            internals.sendText(textarea, 'PASS');
+            const value = textarea.value;
+
+            document.body.removeChild(textarea);
+            return value;
+        });
     });
 </script>