So, you are in a situation where the WordPress system files are damaged, and the last backup was made too long ago. Don't worry if it sounds bad - below you will find detailed step-by-step instructions on how to restore your site in this case.
There are two possible options on how to restore WordPress system files:
Using SSH - this option requires you to connect to your hosting account via SSH and run only 1 command. This option is the easiest and is available on all hosting plans except for Shared Single and WordPress Starter
Using File Manager or FTP - this option is more time-consuming, but will only require you to download and upload files
Whichever option you choose, you do not need to make any changes to the database.
Option 1 - Restoring WordPress system files via SSH
Step 1 - Connect via SSH
First, connect to your account via SSH, and open public_html (or the custom folder where you installed WordPress). For most accounts, the path after connection will be:
cd domains/domain.tld/public_html
Step 2 - Restore files
Once in this folder, run the following command:
backup=WP_`date +%s` && mkdir $backup && mv wp-admin $backup && mv wp-includes $backup && mv *.php $backup && wget https://wordpress.org/latest.zip && unzip latest.zip && rm -rf wordpress/wp-content && mv wordpress/* . && cp -rv $backup/wp-config.php .
Check your website on incognito mode - it should be working by now! If it doesn't, you can restore your website from a backup
Option 2 - Restoring WordPress system files via FTP or File Manager
Step 1 - Preparation
First, you need to create a fresh backup of your website. You can do that by creating a backup using hPanel or by connecting via FTP and downloading the current version of the website.
Step 2 - "Clean" WordPress
Next, you need to go to WordPress.org and download the archive with a clean (no plugins and themes) WordPress. You can find there both the latest version and the older ones - make sure to download the same version that you had!
The unpacked archive will look like this:
Step 3 - Copy WordPress files to hosting
Next, you need to copy all files and folders from the pure WordPress folder to the public_html folder (or another folder that you used to install WordPress).
Open Websites → Manage, search for File Manager on the sidebar and click on it:

Click on Upload:

And select the files and folders of the clear WordPress. When asked, choose Replace:

Alternatively, using FileZilla (or another FTP client of your choice) start uploading WordPress files and when asked, choose Overwrite:
Once the uploading process is done, you can check your website in incognito mode of your browser - it should be working and your plugins, themes, and content will be saved!
NOTE:
If you still find your website not working after doing all the steps, you can restore your website from a backup