To make an Apex method available to a Lightning web component, the developer must follow these considerations1:
* The method must be annotated with the @AuraEnabled annotation, which enables client-side access to the method.
* The method must be either static or part of a global class, and it must be public or global.
* The method must specify the cacheable=true attribute if it only gets data, which enables the method to be invoked at component initialization and improves performance by reducing server round trips.
* The method cannot mutate the result set retrieved from the database, which means it cannot modify, insert, or delete any records. This ensures that the method is idempotent and can be cached safely.
* The method cannot use the @InvocableMethod annotation, which is reserved for methods that are exposed as actions in flows or processes. References:
* 1: Call Apex Methods

The developer should implement a callout from a queueable class called from a trigger to accomplish this. A callout is a request that is sent from Salesforce to an external service, such as a REST endpoint in the ERP system1. A queueable class is an Apex class that implements the Queueable interface and can be executed asynchronously by adding it to the Apex job queue2. A trigger is an Apex script that executes before or after specific data manipulation language (DML) events on a Salesforce object, such as insert, update, or delete3.
The reason why this option is the best is because:
* A callout from a future method called from a trigger (option A) is not recommended, because future
* methods have some limitations, such as not being able to pass sObjects as parameters, not being able to chain future calls, and not being able to monitor the status of the execution4.
* A callout from a schedulable class called from a scheduled job (option B) is not suitable, because scheduled jobs run at a specified time or interval, and not in response to a data change event, such as setting the order status to "Placed"5.
* A flow with a callout from an invocable method (option C) is not feasible, because flows cannot be triggered by data changes, but only by user actions, such as clicking a button, or by process automation tools, such as Process Builder or Workflow.
References:
* 1: Callouts | Apex Developer Guide | Salesforce Developers
* 2: Queueable Apex | Apex Developer Guide | Salesforce Developers
* 3: Triggers | Apex Developer Guide | Salesforce Developers
* 4: Using the Future Annotation | Apex Developer Guide | Salesforce Developers
* 5: Schedulable Interface | Apex Developer Guide | Salesforce Developers
* : [Flow Trigger Workflow Actions | Salesforce Help]