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What happens is perfectly normal. The restoration only reconfigures one site, the main site which is being backed up.

You should exclude the mm4 folder from your backup of your Joomla 3 site.

On your Joomla 4 site you should install Akeeba Backup 9 and back it up separately.

If both sites are sharing a database, remember to exclude each other's database tables in the Database Table Exclusions page.

You can restore the J3 site in the main directory and the J4 site in a subdirectory using the same database in both restorations. The folder structure and the database structure are independent from each other.

I do not generally recommend your intended setup because of three problems you might get tripped over by:

• .htaccess and .user.ini files are inherited across the filesystem (not necessarily the web site URL!) structure. This means that the site in the subdirectory will inherit the .htaccess of the main site. This will lead to problems if you are using Admin Tools' .htaccess Maker and, in fact, may also break SEF URLs even if you're using Joomla's default .htaccess content (shipped as an inert htaccess.txt file).
  
  Solution: Restore the sites to different folders which are not one inside the other.
  
  Also remember that your .htaccess files' RewriteBase needs to change when transferring the site to the domain's root to take it live. Add a note that you need to go to Components, Admin Tools, .htaccess Maker, scroll all the way down, set the site's directory to / and update the HTTP and HTTPS domain names, then click on Save & Create .htaccess — this will take care of this change for you. Better yet, make it a habit to always do that upon every restoration. This might sound like a chore but will save you a LOT of hair pulling down the line. Trust me.
  
  
• Using the same database may lead you to take a backup which includes all database tables, from both installations. This will break one of the two sites when you restore it again in the same database. This is why I told you that you have to exclude each other's tables from the backup.
  
  Solution: use separate databases.
  
  
• You are using the database table name prefix mm4_jos_. This has two distinct problems:
  a. It's too long. The recommended size is 5–7 characters, including the underscore.
  b. It has an underscore in the middle. The underscore indicates the END of the database table name prefix. Having it in the middle of the prefix will cause all sorts of problems.
  
  Solution: Use a table name prefix which is shorter and DOES NOT have an underscore in the middle, consisting only of lowercase letters and numbers e.g. mm4j_.

If you do not heed these recommendations you will most definitely have a bad time, most likely weeks to years later.