Handle quote input (#4762)

Task/Issue URL:
https://app.asana.com/0/414730916066338/1207180035648641/f

### Description
Addresses issue raised here:
#4472

### Steps to test this PR
- [x] Enter a URL in quotes (Or containing a quote)
- [x] Verify that the input is treated as a search term and not a URL

### UI changes
| Before  | After |
| ------ | ----- |

![ddg](https://github.com/user-attachments/assets/4ce49027-1c42-4747-af95-15f27d0a97e0)|![ddg_after](https://github.com/user-attachments/assets/70cbda19-7812-46bf-aeb5-a33fc0b9d7eb)

app/src/test/java/com/duckduckgo/app/global/UriStringTest.kt

@@ -391,7 +391,47 @@ class UriStringTest {
     }
 
     @Test
-    fun whenSchemeIsValidFtpButNotHttpThenNot() {
+    fun whenSchemeIsValidFtpButNotHttpThenIsFalse() {
         assertFalse(isWebUrl("ftp://example.com"))
     }
+
+    @Test
+    fun whenUrlStartsWithDoubleQuoteThenIsFalse() {
+        assertFalse(isWebUrl("\"example.com"))
+    }
+
+    @Test
+    fun whenUrlStartsWithSingleQuoteThenIsFalse() {
+        assertFalse(isWebUrl("'example.com"))
+    }
+
+    @Test
+    fun whenUrlEndsWithDoubleQuoteThenIsFalse() {
+        assertFalse(isWebUrl("example.com\""))
+    }
+
+    @Test
+    fun whenUrlEndsWithSingleQuoteThenIsFalse() {
+        assertFalse(isWebUrl("example.com'"))
+    }
+
+    @Test
+    fun whenUrlStartsAndEndsWithDoubleQuoteThenIsFalse() {
+        assertFalse(isWebUrl("\"example.com\""))
+    }
+
+    @Test
+    fun whenUrlStartsAndEndsWithSingleQuoteThenIsFalse() {
+        assertFalse(isWebUrl("'example.com'"))
+    }
+
+    @Test
+    fun whenUrlContainsDoubleQuoteThenIsFalse() {
+        assertFalse(isWebUrl("example\".com"))
+    }
+
+    @Test
+    fun whenUrlContainsSingleQuoteThenIsFalse() {
+        assertFalse(isWebUrl("example'.com"))
+    }
 }

browser-api/src/main/java/com/duckduckgo/app/browser/UriString.kt

@@ -96,6 +96,9 @@ class UriString {
         }
 
         fun isWebUrl(inputQuery: String): Boolean {
+            if (inputQuery.contains("\"") || inputQuery.contains("'")) {
+                return false
+            }
             if (inputQuery.contains(space)) return false
             val rawUri = Uri.parse(inputQuery)