docs: remove deprecated airbyte-ci references from local-connector-development.md (#75943)

Co-authored-by: Devin AI <158243242+devin-ai-integration[bot]@users.noreply.github.com>

Author: aaronsteers

docs/platform/connector-development/local-connector-development.md

@@ -17,7 +17,6 @@ When developing connectors locally, you'll want to ensure the following tools ar
 1. [`docker`](#docker) - Used when building and running connector container images.
 1. [`gradle`](#gradle) - Required when working with Java and Kotlin connectors.
 1. [Airbyte CDKs](#airbyte-connector-development-kits-cdks) - The Airbyte Connector Development Kit (CDK) tools, including the [`airbyte-cdk` CLI](#the-airbyte-cdk-cli).
-1. [`airbyte-ci` (deprecated)](#airbyte-ci-deprecated) - Used for a large number of tasks such as building and publishing.
 
 ### Poe the Poet
 
@@ -95,14 +94,6 @@ uv tool install --upgrade 'airbyte-cdk[dev]'
 
 For a list of available commands in the `airbyte-cdk` CLI, run `airbyte-cdk --help`.
 
-### airbyte-ci (deprecated)
-
-Airbyte CI `(airbyte-ci`) is a Dagger-based tool for accomplishing specific tasks. See `airbyte-ci --help` for a list of commands you can run.
-
-:::warning
-The Airbyte CI tool is now deprecated and will be phased out shortly. Most airbyte-ci commands have a simpler equivalent in Poe, which you can discover using `poe --help`.
-:::
-
 ## Common Development Tasks
 
 ### Installing Connector Dependencies
@@ -193,7 +184,6 @@ Maintainers can execute any of the following connector admin commands upon reque
 - `/bump-version` - Run the bump version command, which advances the connector version(s) and adds a changelog entry for any modified connector(s).
 - `/format-fix` - Fixes any formatting issues.
 - `/run-connector-tests` - Run the connector tests for any modified connectors.
-- `/run-cat-tests` - Run the legacy connector acceptance tests (CAT) for any modified connectors. This is helpful if the connector has poor test coverage overall.
 - `/build-connector-images` - Builds and publishes a pre-release docker image for the modified connector(s).
 - `/poe` - Run a Poe task.