BaseSystem.dmg could not be copied - not enough disk space

The error message you're seeing suggests that you don't have enough available disk space on your computer to copy the BaseSystem.dmg file.

To resolve this issue, you'll need to free up some space on your hard drive by deleting unnecessary files or moving them to an external storage device. Here are some steps you can take:

1. Check how much free space you have on your hard drive. You can do this by opening Finder, selecting your hard drive, and clicking "File" > "Get Info." Look for the "Available" section to see how much space you have left.
2. Delete any unnecessary files or folders. Go through your files and folders and delete anything you don't need or can easily download again in the future. Be sure to empty your Trash once you're done to permanently delete the files.
3. Move large files to an external storage device. If you have large files that you don't need to access regularly, consider moving them to an external hard drive or USB drive to free up space on your main hard drive.
4. Remove any Time Machine local snapshots.

Try booting into Safe Mode.

You are booting from a very old version of macOS (installer) in that picture. Older versions of macOS don't understand the new drive layouts or file systems utilized by later versions of macOS (10.13+). Try booting into Internet Recovery Mode using Command + Option + R to see if you can access the Big Sur online installer. Unfortunately for some Macs they will only boot to the older macOS online installer regardless of the keys used to access Internet Recovery Mode.

If you have access to another compatible Qualifying Mac, then you can create a bootable macOS 11.x Big Sur installer using the instructions in this Apple article:

Create a bootable installer for macOS - Apple Support

A compatible Qualifying Mac for Big Sur is generally one from 2013 to 2020, but you can use the contents of this article to confirm:

https://eshop.macsales.com/guides/Mac_OS_X_Compatibility

If you do not have enough free space on the internal SSD, then you probably won't be able to use Internet Recovery Mode or a bootable USB installer to install Big Sur because these require even more free space to be available than running it from within macOS. You could install Big Sur to an external drive which you can then boot to the external drive in order to attempt to free up space on the internal drive, or to transfer any important data from the internal drive before completely erasing the internal drive. Or if you can only boot this older macOS installer, then install it to the external drive, then upgrade macOS on the external drive so you can access the internal drive.

FYI, people should always have frequent and regular backups of their computer and all external media (including the cloud) which contains important & unique data. It is also a good idea to make sure to have a current backup just before attempting to upgrade the OS or before making any other significant changes to the system.

HWTech gave you a few valuable options worth trying. If, at all, it doesn't work I would advise to stop the computer by holding the Power button down, if there is no message appearing "Are you sure that you want to shut your computer down?" , just keep on pressing the Power button until it goes dark. Try to start-up in local Recovery mode by holding Command + R when powering up. Yu may also hold down Command + Option + R, which brings you to internet recovery. Either way you should be able to restore your original software. After which you can review your disk space.

At this point, you will need to boot up in Recovery Mode, and try reinstalling macOS.

Ref: Use macOS Recovery on an Intel-based Mac - Apple Support

1) Did you not make a Time Machine or other backup?

2) Try clicking on Mount to see if "disk0s2" mounts; if it does, tell us how much space there is.

If not, and you have no backup, then I am afraid your data is lost.