Remove some miscellaneous references to Cirrus. (#161390)

Towards https://github.com/flutter/flutter/issues/161387.

... made a few TLC changes the best I could.

dev/bots/README.md

diff --git a/dev/bots/README.md b/dev/bots/README.md
index 01b151b..9a080da 100644
--- a/dev/bots/README.md
+++ b/dev/bots/README.md
@@ -2,23 +2,22 @@
 
 This directory exists to support building Flutter on our build infrastructure.
 
-Flutter build results are available at:
-* https://flutter-dashboard.appspot.com/#/build
-  - Aggregate dashboard of the separate CI systems used by Flutter.
-* https://cirrus-ci.com/github/flutter/flutter/master
-  - Testing is done on PRs and submitted changes on GitHub.
+Flutter build results are available at: <https://flutter-dashboard.appspot.com>.
 
 Flutter infra requires special permissions to retrigger builds on the
 [build dashboard](https://flutter-dashboard.appspot.com/#/build). File an
 [infra ticket](../../docs/infra/Infra-Ticket-Queue.md) to
 request permission.
 
-The [Cirrus](https://cirrus-ci.org)-based bots run the [`test.dart`](test.dart)
-script for each PR and submission. This does testing for the tools, for the
-framework, and (for submitted changes only) rebuilds and updates the main
-branch API docs [staging site](https://main-api.flutter.dev/).
+The [LUCI](https://chromium.googlesource.com/infra/luci/luci-py/+/refs/heads/main/README.md)-based
+bots run the [`test.dart`](test.dart) script for each PR and submission. This
+does testing for the tools, for the framework, and (for submitted changes only)
+rebuilds and updates the main branch API docs [staging site](https://main-api.flutter.dev/).
 For tagged dev and beta builds, it also builds and deploys the gallery app to
-the app stores. It is configured by the [.cirrus.yml](/.cirrus.yml).
+the app stores. It is configured by two `.ci.yaml` files:
+
+- framework: [`.ci.yaml`](../../.ci.yaml)
+- engine: [`engine/src/flutter/.ci.yaml`](../../engine/src/flutter/.ci.yaml)
 
 The build dashboard includes post-commit testing run on physical devices. See
 [//dev/devicelab](../devicelab/README.md) for more information.
@@ -134,7 +133,6 @@
    `$ cd ../..`
    `$ dev/bots/upload_android_tools.py -t ndk`
 
-
 ## Flutter codelabs build test
 
 The Flutter codelabs exercise Material Components in the form of a

dev/tools/create_api_docs.dart

diff --git a/dev/tools/create_api_docs.dart b/dev/tools/create_api_docs.dart
index 33cd878..deb6e2b 100644
--- a/dev/tools/create_api_docs.dart
+++ b/dev/tools/create_api_docs.dart
@@ -401,7 +401,7 @@
     // show the end of it if there was a problem.
     print('${DateTime.now().toUtc()}: Building Flutter docset.');
 
-    // If dashing gets stuck, Cirrus will time out the build after an hour, and we
+    // If dashing gets stuck, LUCI will time out the build after an hour, and we
     // never get to see the logs. Thus, we run it in the background and tail the
     // logs only if it fails.
     final ProcessWrapper result = ProcessWrapper(

docs/contributing/testing/Running-and-writing-tests.md

diff --git a/docs/contributing/testing/Running-and-writing-tests.md b/docs/contributing/testing/Running-and-writing-tests.md
index 51ffb01..a191c20 100644
--- a/docs/contributing/testing/Running-and-writing-tests.md
+++ b/docs/contributing/testing/Running-and-writing-tests.md
@@ -42,7 +42,7 @@
 paused state and wait for connection from a debugger. This option lets you set breakpoints
 before the test runs.
 
-To run analysis and all the tests for the entire Flutter repository, the same way that Cirrus
+To run analysis and all the tests for the entire Flutter repository, the same way that LUCI
 runs them, run `dart dev/bots/test.dart` and `dart --enable-asserts dev/bots/analyze.dart`.
 
 If you've built your own flutter engine (see [Setting up the Engine development environment](../../engine/contributing/Setting-up-the-Engine-development-environment.md)), you