MacBook Pro: Storage Full, Won't Boot, Apple Logo w/Spinning Wheel, No Safe Mode, EFI Boot Issue?

If you are booting into Verbose Mode, then the Mac is booting macOS so don't worry about any EFI boot file. If the boot process never makes it to the Desktop, then you have some sort of software issue either with macOS or a third party driver/app or possibly a hardware issue. Try reinstalling macOS over top of itself.

Try running Disk Utility First Aid and check the details for unfixed errors even if it completes as "OK". If there are any unfixed errors listed, then you will need to erase the whole physical drive before reinstalling macOS or restoring from a backup.

Otherwise make sure you have a good verified working backup and perform a clean install of macOS by first erasing the whole physical drive as mentioned by @Kappy. Here is how you erase the physical drive:

https://support.apple.com/en-us/HT208496

Test the laptop with a clean install before migrating or restoring from a backup and before installing any third party apps. If a clean install doesn't work correctly, then you have a hardware issue of some sort.

It also never hurts to run the Apple Diagnostics.

If you have a Disk Full problem, then the only solution is to reformat the drive. All your data on the drive will be erased, so you will need a recent backup for recovery.

Preventing Disk Full Error

First: Get Correct Storage Information.Do not use the information from the Storagesection of the About This Mac dialog. Ignore the Storage information as it is typically wrong. To find out the correct information for any disk: Select a Desktop disk icon. Press Command-I to open the Get Info window and look at the topmost panel displayed. You will find the disk information displayed for Capacity, Available, and Used. If you have more than one disk/partition then repeat for each one on your Desktop.

Second: be aware of available storage space. You need to leave at least 20GBs of free space on your startup volume.

Third: get rid of files you don't need by deleting them or storing them on another drive so you can remove them on the startup volume.

How to Free Up Space on The Hard Drive

1. 1. You can remove data from your Home folder except for the /Home/Library/ folder.
   2. Visit The XLab FAQsand read the FAQ on freeing up space on your hard drive.
   3. Also, see Freeing space on your Mac OS X startup disk.
   4. Free up storage space on your Mac.
   5. See Where did my Disk Space go?.
   6. Be sure to Empty the Trash to recover the space.
   7. Replace the drive with a larger one. Check out OWC for drives, tutorials, and toolkits.
   8. Use OmniDiskSweeper or GrandPerspectiveU to search your drive for large files and where they are located.

Fourth: if you cannot delete files or put files in the Trash without errors, then that means your drive has been corrupted because you over-filled it. You will need to erase the drive and reinstall macOS. I'm afraid you will lose all of your data, if it hasn't been backed up already.

What Happens If A Disk Becomes Full

Allowing the disk to become full causes the directory to become too corrupted for repair. The current directory space was too small for all the files you were saving. In order to enlarge the directory, the OS must assign existing and contiguous space for a larger directory. But there is not enough space available for this. So, the operation fails and leaves the drive in an abnormal and unrepairable state. The only "fix" is to erase the drive and start over. You cannot backup your files first nor can you delete files to make space. The disk is FUBAR. If you don't have your data backed up then it will be erased and lost.

What do you do? You must reformat the drive using Disk Utility. If you are fortunate, the Recovery HD is still bootable:

Install El Capitan or Later from Scratch

     If possible backup your files.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo appears. When the Utility Menu appears:
2. Select Disk Utility from the Utility Menu and click on Continue button.
3. When Disk Utility loads select the volume (indented entry, usually Macintosh HD) from the Device list.
4. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
5. Set the Format type to APFS (only if running Catalina on an SSD) or Mac OS Extended (Journaled.)
6. Click on the Apply button, then wait for the Done button to activate and click on it.
7. Quit Disk Utility and return to the Utility Menu.
8. Select Install OS X and click on the Continue button.

This will install the version of OS X you had installed.

The OS does not have anything stored in the EFI on the drive. The boot file is in ROM, and is burned in at the factory. I'm not sure how it would be overwritten or changed. Only those who are booting a hackintosh use the EFI on the drive for the startup code by intercepting the code from the boot ROM. macOS retains the EFI but does not use it.

Technically there is an .efi file within the System Folder which is used for booting macOS. Regardless the OP is booting into Verbose Mode so the bootloader is not the problem.

I started with the OP but did not see your post until I already replied. You "stepped over" me by answering long before I got back to the topic. Since the OP addressed his query at me, it would have been impolite of me not to reply. 😎

In Mojave and Catalina there is no ".efi" file. There is only a number of "boot.efi" files. I don't know when the ".efi" was removed. I have no systems older than Mojave.