Colored_console_log=False not affecting all Airflow processes

### Apache Airflow version

main (development)

### If "Other Airflow 2 version" selected, which one?

_No response_

### What happened?

I was attempting to disable colored logs that we have with the new struct logging (since where I'm uploading the logs doesn't support colors and the show as terminal escape sequences which are difficult to read). But when setting `AIRFLOW__LOGGING__COLORED_CONSOLE_LOG=False` only some of the Airflow processes respect this configuration. The API server and Triggerer seem to ignore the disabled colors.

#### Color Enabled:

#### Color Disabled:

### What you think should happen instead?

All processes should log to stdout with no color

### How to reproduce

Start and Airflow environment with and without this option set and observe the differences (in my case I used breeze).

### Operating System

Linux Dockerized

### Versions of Apache Airflow Providers

_No response_

### Deployment

Docker-Compose

### Deployment details

_No response_

### Anything else?

_No response_

### Are you willing to submit PR?

- [x] Yes I am willing to submit a PR!

### Code of Conduct

- [x] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

Start by reproducing the colored and uncolored configurations in the Dockerized Airflow environment, using breeze if available, and compare stdout from the API server and Triggerer with other processes. Done means AIRFLOW__LOGGING__COLORED_CONSOLE_LOG=False consistently produces color-free logs from all Airflow processes.

Written by the indexing model from the issue text.