I’ve migrated apps, data sources, associated Apps Script projects, etc., across accounts like you describe. Some pieces were more straightforward than others–especially when transferring from a personal account to a Workspace account. I don’t have experience transferring between accounts across Workspaces. Basically, the techniques to try are:
Transfer ownership directly if you can (e.g., this works for apps themselves)
If that doesn’t work and you don’t need to change explicit file ownership, try sharing the file from the source account to the target account.
If necessary, share the file from the source account to the target account, copy the file in the target account, and then update the app’s reference to the new file.