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You mentioned that you tried to use Run Test but I have to note that we have explicitly documented that you cannot use Run Test, and explained the reason why it's not possible:

Tempting as it may be DO NOT try to use the Run Test button next to the backup task. It does nothing for backup tasks; it returns immediately. This is expected and it does NOT mean that your backup task is broken. You will have to wait for it to run for real. Yes, it's a bit confusing but the Run Test button was only really designed to work with very short tasks which complete in a single shot, not resumable tasks which run over a long period of time. Backup tasks are resumable tasks exactly because they need to run over a long period of time!

Speaking of the documentation, I will note that everything you are asking is already documented. I have written this documentation myself. I know what I put in there, how I phrased it, and why. In short, it was to prevent this kind of issue which stems from a deep misunderstanding of what Joomla Scheduled Tasks can do and what is their practical use case with regards to taking backups. Please do read it again, carefully; don't skim through it. It will disabuse you of the notion that you can use Scheduled Tasks instead of a CRON job. It is used with a CRON job, the major difference being that it's one CRON job you only ever need to update when you upgrade your site's PHP version, allowing you to handle all the backup scheduling within Joomla itself, something that has some distinct benefits in certain use cases – but I'll get back to that in a minute.

I want you to first understand something important.

Taking a backup requires running some PHP code. PHP code does not run by itself; it needs something to tell it to run (a "controller"). Joomla Scheduled Tasks can act as a controller; however, the task scheduler (the part of Joomla which figures out which, if any, scheduled task to execute next) is itself a piece of PHP code. Therefore, you need something to tell the task scheduler to run so it can act as a controller for the actual scheduled tasks which execute the tasks.

Think of scheduled tasks as workers in a warehouse. If nobody tells them what to do, they sit around doing nothing even though their nominal function is to pick orders, pack them up, and stick shipping labels on them. That is to say, the inherent role of the worker does not magically lead to work being carried out unless the worker is explicitly told to perform a certain task within their role. The task scheduler is pretty much the warehouse foreman; he tells workers what to do. However, the foreman cannot issue any orders to workers unless the accounting department sends him orders to fulfil. Without any orders to fulfil, he and his crew are idle. So, what would be the equivalent for scheduled tasks? Something that tells the task scheduler to execute, checking its list of scheduled tasks and their settings, telling them what to do. That's the bit you are either misunderstanding or completely missing.

Joomla gives you three ways to tell its task scheduler to run: run a CLI CRON job, use a URL with a web-based CRON job, and Lazy Scheduling. The first two require a CRON job. The latter requires a reliable, constant flow of traffic to your site. Not just a few hundred page loads a day; we are talking about several hundred to thousands of page views per hour, roughly evenly spread out throughout the hour, 24 hours a day, 7 days a week. When there's no traffic, the Lazy Scheduler does not run. Even when it runs it has a lot of caveats and issues; please read the documentation where I explain those and why you should never rely on Lazy Scheduling to take backups.

The bottom line is that you will have to use a CRON job to tell the task scheduler to run, and the task scheduler will tell scheduled tasks to run.

So, why bother with Scheduled Tasks instead of just setting up a backup CRON job? There are pragmatic use cases for it. If there were none, I would not have bothered writing the code to do the integration, nor would have I spent my time to test this feature as it was developed and provide my feedback back to Joomla. Here are two use cases where using Scheduled tasks makes sense.

If you want to manage several scheduled maintenance tasks on your site besides taking backups it makes sense to create one CRON job running every minute to trigger Joomla's task scheduler on each site, then set up all your maintenance tasks (including backups) as Joomla Scheduled Tasks. Managing the tasks in Joomla is far easier than wrangling stray CRON jobs (better user experience).

If you want people with administrative (Super User) access to your site to manage the backup schedule without giving them access to the hosting control panel it makes sense to create one CRON job running every minute to trigger Joomla's task scheduler on each site, then set up your backups as Joomla Scheduled Tasks. Scheduled Tasks allows you to move the maintenance task scheduling privileges into Joomla instead of having to give full control over the hosting account (principle of least privilege).

I do not have enough information about your use case to tell you if Joomla Scheduled Tasks are a good fit for you or not. Hopefully, reading this reply you have a better picture of what is technically possible and when it makes sense from an operations point of view to use them. If you have questions, I will be happy to answer them.