You transferred your 2015 MacBook Air to the new M5 MacBook Air using Migration Assistant, but approximately 80 GB stored on your separate Data_vol did not appear on the new Mac.
Apple’s current Migration Assistant documentation says it can transfer user accounts and their selected contents, as well as Other Files & Folders.
It can also transfer information from another disk, a Time Machine backup, or other storage device. (Apple Support)
Therefore, I would not assume that Data_vol was necessarily excluded simply because it was a separate volume.
Before copying anything, check the new Mac in Finder under Go >> Go to Folder >> /Volumes to see whether Data_vol is mounted.
Also check ~/ and your migrated account.
On the old Mac, open Disk Utility >> View >> Show All Devices and verify that Data_vol is still present and that the approximately 80 GB remains there.
If the data is still on the old volume, there is another option worth considering before manually copying it: run Migration Assistant again and examine exactly what it offers under Other Files & Folders.
This could determine whether the existing Data_vol contents can be transferred without creating a separate permanent duplicate. Apple says Migration Assistant can be run after initial setup. (Apple Support)
For the eventual organization of the data, you have two reasonable choices. You can place it in a folder such as:
/Users/your-account/Data/
or recreate Data_vol as a separate APFS volume.
Data is simply a folder you create; it has no special macOS status. APFS supports multiple volumes within a container and shares available storage between them.
A separate volume is therefore a matter of organization rather than a requirement of macOS. It also does not constitute a backup, because a second volume on the same physical SSD remains dependent on that SSD.
For future protection, verify specifically that the location containing your data is included in Time Machine.
Apple documents that Time Machine can restore files to the same Mac or another Mac, and Apple’s technical documentation provides for backing up all mounted volumes or limiting backups to the startup volume. (Apple Support)
So the sequence I would use is: first determine whether Data_vol is still present and whether its 80 GB remains intact; then check what Migration Assistant offers under Other Files & Folders; then decide whether the data should remain a separate APFS volume or become a folder within your user account. There is no reason to create a second permanent copy until those questions have been resolved.
Apple documentation: Transfer your information to Mac from another computer or device · Transfer to a new Mac with Migration Assistant · Back up your Mac with Time Machine
One other detail is worth emphasizing: if your immediate objective is avoiding duplication, I would investigate a second Migration Assistant run before manually copying the 80 GB. Apple explicitly provides an Other Files & Folders selection, so that is the most relevant part of Migration Assistant to examine in your particular case. (Apple Support)