I can't update to 10.15.4.

Hmmm. There is no 12.15.3 version of macOS. Did you mean 10.15.3? I would start by suggesting that you repair the drive:

Repair the Drive for El Capitan or Later

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility and press the Continue button.
3. Then select the indented (usually, Macintosh HD) volume entry from the side list. 
4. Click on the First Aid button in the toolbar and wait for the Done button to activate. Click on it, then quit Disk Utility.
5. Select Restart from the Apple menu.

Now, try re-running the update. If you still have a problem, then Download and Install the macOS Catalina 10.15.4 Combo Update.

In the future: I grasp that you are Italian but I cannot always figure out what is in the dialogs. An interpretation would be helpful for any important terms I might need to know. I'm mono-lingual. Thanks. Oh, I did get this one.

Get Correct Storage Information

Do not use the information from the Storage section 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.

The categories found in the Storage section of About This Mac is simply an arbitrary way of displaying files on your drive. There are no such categories actually on the drive.

If you only had 8GBs of free space to update macOS, then you are quite a few GBs short. You should have at least 15-30GBs free space to upgrade or update macOS. No wonder you were having a problem.

The combo updater is usually the quickest and safest way to update. If available I will use it over the System/Software Update preference pane method.

After downloading the updater exactly what happened and what did you do? Did you run the updater?

I happen to know that dialog pretty well, so not a problem. Thanks for understanding.