Data files got corrupted after installing Ventura OS and running Migration Assistant

The correct method of using Migration Assistant is noted below, by correct I mean it is the fastest, most trouble free and reliable method:

·       Always connect your old Mac's Time Machine External Hard Disk, this will allow a migration from your TM backup and it will be dead simple! When you start the new Mac for the first time it will startup Setup Assistant (SA), SA will get to a point where it asks if you are migrating from another computer, select Yes and follow the on-screen prompts and it's done! It is that simple! This is the easiest, quickest and most reliable method to migrate from the old Mac to the new Mac is to simply connect the old Mac's Time Machine External Hard Disk to the new Mac using a USB cable before you turn on the new Mac. 

·       NOTE 1: You will likely need a USB A to USB C adapter, you can find them on Amazon for $10 or less.

·       NOTE 2: If you have already done SA on the new computer then simply connect the Time Machine External Hard Disk using a USB cable and launch Migration Assistant (MA) which is located in Applications - Utilities - MA. Then follow the on-screen prompts.

·       The ONLY difference between MA and SA is MA will create a new user account that you need to log into.

Both SA and MA migrate applications (not 32 bit apps), data files & settings. They do not migrate Mac OS itself. Some professional apps such as Adobe and Microsoft apps may require re-installing their apps as they will not allow them to be migrated. As long as you kept the security keys for installing their apps, it is not an issue. 

Finally, never EVER use Wi-Fi when doing Setup Assistant or Migration Assistant. Why, it simply fails in most cases. Please read and follow the directions in Setup Assistant and Migration Assistant. If you do not have a Time Machine backup of the older Mac then create one! If you are not aware of Time Machine, please read Back up your Mac with Time Machine and finally if you need an External Hard Disk to use as a Time Machine External Hard Disk then many experience users on these forums prefer the OWC Mercury Elite Pro due to it's reasonable price, high level of quality and ease of use. 

As we have zero idea of how you executed your migration then I'm pretty sure you just made a goof along the way.

In addition it is extremely rare that someone has to do an erase and install.

Last... do you have any of the following third party apps installed on your Mac?

       •      Antivirus Apps

       •      Cleaning Apps

       •      Security Apps

       •      VPN Apps

       •      Maintenance Apps

If so, I can say almost certainly that is the source of you issues as these types of third party apps at best are 100% worthless and at worst damaging to Mac OS, make Mac OS appear unstable, make Mac OS slow and in return offer absolutely nothing in return that Mac OS cannot already do!!!

What macOS version was running on the iMac and backed up, before erasing and installing a fresh version of Venture...?

Time Machine works wonders for Migrating back to the same macOS version and to a later macOS version.

Time Machine does not work well for Migrating backwards to an earlier macOS version.

My advice, start over and reinstall the macOS version that you had, then Migrate from the Time Machine backup.

Which is why it’s always wise to check your applications for potential compatibility problems before upgrading the OS.

Okay, well my preference is to use Time Machine just as Apple originally intended. In short to backup everything and let iCloud be used for what it is intended for which is to synch data between devices. My experience is when people think out of those boxes it tends to create confusion and errors which I’m not trying to accuse you of. Regarding your app compatibility issue, is there a reason you cannot keep the third party apps updated so as you update Mac OS they will work as they should?

just suggesting this as I seen so many users that try to keep their systems static eventually run into very difficult compatibility issues at some point.

Best!

Bingo! You're welcome.