How to clean : APPLE SSD AP0512Q Media

A good place to start is to do "About the Mac.." from your Apple menu. In the resulting window, click the "storage" tab.

There you will find a "Manage..." button that will walk you through some of the big space users and suggest how to deal with them.

Basically the only safe way you can free up space is to delete USER data by putting it on some non internal drive and then deleting what you copied.

If you delete large blocks of data, Apple may sequester it as Purgeable Space. Apple states it looks lost to you but is actually available when needed.

I use the paid version of Daisy Disk to reduce Purgeable.

Within Disk Utility, click on the "Macintosh HD" on the left pane. On the right pane, look for the value next to "Free". This is the really important value. If "Free" says you actually have 318GB free as implied by your screenshot and you are running out of free storage space, then you don't have the proper size SSD for your workload if you are getting errors related to storage space. Seems like 300GB free should be enough for many workloads, but it may depend on the size of videos you are processing. We definitely need more details like this.

What is the exact error message you are encountering? Could it be a memory issue instead of storage issue?

Running EtreCheck and posting the report here may be useful so that we can get some details about your computer and its performance metrics and summaries of the system logs.

The image you posted in the first message, shows how the PHYSICAL device is divided up among the various Containers. That top-level display tells you NOTHING about MacOS Volumes and nothing about practical free space.

To see more, you need to drill down the hierarchy until you find the Macintosh HD Data Container. That will start to give you gross ideas of free space, which should be more comparable to the other displays.

The image posted shows over 300 GB of available storage. Sometimes the "Other" (medium gray) category includes data that can be purged, but it can be stuff that is real. Also - it might take some time to settle down. I just checked mine and it was saying about 192 GB, but after waiting a bit, it parsed it into other categories where now Other is just about 53 GB.

I haven't really tried it with a Mac, but I'm thinking that it might be possible to recover from a backup where some of the overhead that doesn't clear by itself just vanishes into the ether. It would be rather drastic though.

But again - it looks like there's more than 300 GB of free storage, so if there's a problem it might be with a specific application and not that there's actual lack of available storage.

Sure. Looking at the top-level physical drive isn't going to say much other than the size of the drive and how much is taken by secondary (recovery?) volumes. It would really require selecting "Macintosh HD" in the sidebar to see what the available storage is, but we've already seen something more detailed from the Storage tab of About This Mac.

That's showing that most of the storage capacity is unused/available.

Are you seeing a specific message saying that there isn't enough available storage capacity? I've seen that a few times when I had hundreds of GB of available storage, such as when I was trying to do an iOS update on an iPhone but it refused to do it.

So what are you seeing that says there isn't enough storage?

I was just adding what I saw about what seemed out of whack in the first display, but it turns out is as expected.

It does seem like there is lots of free space where it is needed, so I am puzzled as well about what the problem might be.

The OP has plenty of available storage, so I'm not sure what the problem is.