Track-It! 11.x attachments are saved on the drive, with the default directory of C:\Program Files(x86)\BMC Software\Track-It!\Track-it! Services\FileStorageData\Repositories
These files are not part of the normal backup process and may or may not be migrated, depending on a variety of things. See https://docs.bmc.com/docs/trackit2018/en/migrating-to-track-it-2018-777225386.html for details.
Track-it! 2018 saves documents in the database, but is limited to 29 MB per document.
The issue ended up being a faulty DLL. Support replaced the NAMLogicAttach.dll file with a copy they provided. After that, attachments which were migrated from 11.4 were able to open.