Hi @Jose Perez , welcome to Microsoft Q&A forum.
A database transaction unit (DTU) represents a blended measure of CPU, memory, reads, and writes. External tables do read the data from the remote databases and hence impact the database performance. You rightly pointed out scaling up the historical database during the migration process will help, but if huge data is being retrieved from the production database, it could throttle the requests still. So scaling has to be done at both for a smoother transition.
On a side note, I would suggest you to use SQL Data Sync service for migration. You can refer to below links for more details.
https://video2.skills-academy.com/en-us/azure/azure-sql/database/sql-data-sync-data-sql-server-sql-database
https://video2.skills-academy.com/en-us/azure/azure-sql/database/sql-data-sync-agent-overview
Please let me know if you need more details and we can discuss further.
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