Have you reviewed this link: Microsoft 365 tenant-to-tenant migrations
In the Tenant-to-tenant migration architecture model it discusses about several scenarios and the general steps.
While in this case, to me I suppose you may need another domain for migration.
Since it would be necessary in mailbox migration.
Reference: Cross-tenant mailbox migration (preview)
Later once the migration is done, you may verify your old domain in the new tenant.
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