The only thing that could have gotten in your way is the .htaccess Maker but it includes an exception for the Joomla Update files out of the box. It's possible that you accidentally removed it. Let's make sure this is not the case or, if it is, fix it.
Go to Components, Admin Tools.
Click on .htaccess Maker.
Find Allow direct access to these files
Make sure there is a line reading administrator/components/com_joomlaupdate/restore.php
. If not, add it now.
Click on Save and Create .htaccess in the toolbar at the top of the page.
If this did not help the problem does not come from Admin Tools. You would need to contact your host about it. A very likely issue is that your host's server configuration (most likely a mod_security2 rule) is blocking the request Joomla Update's JavaScript code makes to the administrator/components/com_joomlaupdate/restore.php
file. This file is what extracts the update ZIP file Joomla has downloaded and triggers the update finalisation code after the extraction is over.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!