Increase subsharding for Linux tool_integration_tests (#158196)

I've noticed Linux tool_integration_tests 5_5 has come very close to timing out. See https://github.com/flutter/flutter/issues/155317 for more context, I am not 100% confident that increasing the subsharding here will help given that we just very recently increased subsharding from 4 to 5, but the results could be interesting regardless.

<details>

<summary> Pre-launch checklist </summary> 

</details>

.ci.yaml

@@ -1201,7 +1201,8 @@ targets:
       - bin/internal/engine.version
       - .ci.yaml
 
-  - name: Linux tool_integration_tests_1_5
+  - name: Linux tool_integration_tests_1_6
+    bringup: true
     recipe: flutter/flutter_drone
     timeout: 60
     properties:
@@ -1217,7 +1218,7 @@ targets:
           {"dependency": "open_jdk", "version": "version:17"}
         ]
       shard: tool_integration_tests
-      subshard: "1_5"
+      subshard: "1_6"
       tags: >
         ["framework", "hostonly", "shard", "linux"]
       test_timeout_secs: "2700"
@@ -1227,7 +1228,8 @@ targets:
       - bin/**
       - .ci.yaml
 
-  - name: Linux tool_integration_tests_2_5
+  - name: Linux tool_integration_tests_2_6
+    bringup: true
     recipe: flutter/flutter_drone
     timeout: 60
     properties:
@@ -1243,7 +1245,7 @@ targets:
           {"dependency": "open_jdk", "version": "version:17"}
         ]
       shard: tool_integration_tests
-      subshard: "2_5"
+      subshard: "2_6"
       tags: >
         ["framework", "hostonly", "shard", "linux"]
       test_timeout_secs: "2700"
@@ -1253,7 +1255,8 @@ targets:
       - bin/**
       - .ci.yaml
 
-  - name: Linux tool_integration_tests_3_5
+  - name: Linux tool_integration_tests_3_6
+    bringup: true
     recipe: flutter/flutter_drone
     timeout: 60
     properties:
@@ -1269,7 +1272,7 @@ targets:
           {"dependency": "open_jdk", "version": "version:17"}
         ]
       shard: tool_integration_tests
-      subshard: "3_5"
+      subshard: "3_6"
       tags: >
         ["framework", "hostonly", "shard", "linux"]
       test_timeout_secs: "2700"
@@ -1279,7 +1282,8 @@ targets:
       - bin/**
       - .ci.yaml
 
-  - name: Linux tool_integration_tests_4_5
+  - name: Linux tool_integration_tests_4_6
+    bringup: true
     recipe: flutter/flutter_drone
     timeout: 60
     properties:
@@ -1295,7 +1299,7 @@ targets:
           {"dependency": "open_jdk", "version": "version:17"}
         ]
       shard: tool_integration_tests
-      subshard: "4_5"
+      subshard: "4_6"
       tags: >
         ["framework", "hostonly", "shard", "linux"]
       test_timeout_secs: "2700"
@@ -1305,7 +1309,8 @@ targets:
       - bin/**
       - .ci.yaml
 
-  - name: Linux tool_integration_tests_5_5
+  - name: Linux tool_integration_tests_5_6
+    bringup: true
     recipe: flutter/flutter_drone
     timeout: 60
     properties:
@@ -1321,7 +1326,34 @@ targets:
           {"dependency": "open_jdk", "version": "version:17"}
         ]
       shard: tool_integration_tests
-      subshard: "5_5"
+      subshard: "5_6"
+      tags: >
+        ["framework", "hostonly", "shard", "linux"]
+      test_timeout_secs: "2700"
+    runIf:
+      - dev/**
+      - packages/flutter_tools/**
+      - bin/**
+      - .ci.yaml
+
+  - name: Linux tool_integration_tests_6_6
+    bringup: true
+    recipe: flutter/flutter_drone
+    timeout: 60
+    properties:
+      add_recipes_cq: "true"
+      dependencies: >-
+        [
+          {"dependency": "android_sdk", "version": "version:35v1"},
+          {"dependency": "chrome_and_driver", "version": "version:125.0.6422.141"},
+          {"dependency": "clang", "version": "git_revision:5d5aba78dbbee75508f01bcaa69aedb2ab79065a"},
+          {"dependency": "cmake", "version": "build_id:8787856497187628321"},
+          {"dependency": "goldctl", "version": "git_revision:2387d6fff449587eecbb7e45b2692ca0710b63b9"},
+          {"dependency": "ninja", "version": "version:1.9.0"},
+          {"dependency": "open_jdk", "version": "version:17"}
+        ]
+      shard: tool_integration_tests
+      subshard: "6_6"
       tags: >
         ["framework", "hostonly", "shard", "linux"]
       test_timeout_secs: "2700"