Hey there. When you cross-save, you choose an active account, which then becomes the profile you log into on all linked platforms.
If you set up your PSN account as the active one, then your PSN characters will be the ones you see when you log into Steam. Your Steam characters will be made dormant. So it would not be possible to cross-save the PSN veteran status over while still keeping your Steam characters and progress.
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thanks for the clarification