How to mount Internal Storage as USB Mass Storage for recovering data?
You can't do that. Google has made MTP the default since version 3.0 and remove mass storage mode completely years ago in Android 4.0


No USB MASS STORAGE Support!!? Only MTP PTP?
Enabling USB Mass Storage in Android Kitkat 4.4.2 
Any way to get USB Mass Storage instead of MTP?
Why Do New Versions Of Android Not Support USB Mass Storage Mode?


If you want to do things directly on the data partition you have 2 ways


Run command in adb shell
Start in recovery mode (if you're using a custom ROM)


Since you're running a restore from backup, I assume you're on a custom ROM and still have the backup file with you, why don't just do the restoration again?