MySql Deadlock in check_trigger_timeouts

### Apache Airflow version

Other Airflow 2/3 version (please specify below)

### If "Other Airflow 2/3 version" selected, which one?

2.10.5

### What happened?

Hi,

We got the exact same error as: #41429, it looks to me that we should wrap the `execute` method in `check_trigger_timeouts` so we catch the exception and can actually retry? like `adopt_or_reset_orphaned_tasks` does.

This happened for the first time shortly after we added a second triggerer instance, so this could make this issue more likely.

Thanks
Sylvain

### What you think should happen instead?

_No response_

### How to reproduce

running a scheduler and multiple triggerer.

### Operating System

Fedora 8.3

### Versions of Apache Airflow Providers

_No response_

### Deployment

Official Apache Airflow Helm Chart

### 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 locating the check_trigger_timeouts entry point and compare its execute flow with adopt_or_reset_orphaned_tasks, especially how exceptions are handled. Reproduce the deadlock with a scheduler and multiple triggerers, then verify that the timeout check can retry after the reported MySQL error.

Written by the indexing model from the issue text.