Async-safe mass delete of children with Batch

Question

How to write in Apex a mass deletion (over 10 000 records, even up to 150 000) of related records that can be safely called from async context, like Batch?

I have two custom objects, lets call them Source__c (Parent) and Payment__c (Child). They are connected using Lookup relation. Upon deletion of a Source__c records, I need to delete all related Payments. For now, I'm using simple Batch that is executed from a before delete trigger. In the future, there might be a batch that will delete a Source record, and it should delete the Payments as well, but batch cannot be executed from another batch besides chaining in finish(). How to approach this safely, either by chaining the deletion somehow or making clear, async-safe exception to prevent such batch from running?

My code currently, part of trigger handler:

public with sharing class SourceTH extends TriggerHandler.DelegateBase {


    public override void prepareBefore() {
        if (Trigger.isDelete) {
            deleteRelatedPayments(Trigger.oldMap.keySet());
        }
    }

    private static void deleteRelatedPayments(Set<String> sourceIds) {
        if (!System.isFuture() && !System.isBatch()) {
            DeletePaymentsOnSourceBatch.runBatch(sourceIds);
        }
        else {
            // How to make mass delete safely from async context?
        }
    }
}

Batch class to delete:

public with sharing class DeletePaymentsOnSourceBatch implements Database.Batchable<SObject> {

    private final Set<String> sourceIds = new Set<String>();

    public static void runBatch(Set<String> sourceIds){
        Database.executeBatch(new DeletePaymentsOnSourceBatch(sourceIds), 100);
    }


    public Database.QueryLocator start(Database.BatchableContext BC) {
        return Database.getQueryLocator([
                SELECT Id
                FROM Payment__c
                WHERE Source__c IN :this.sourceIds
        ]);
    }

    public void execute(Database.BatchableContext BC, List<SObject> scope) {
        delete scope;
    }

    public void finish(Database.BatchableContext BC) {}


}