Issue migrating from SQL Server 2008 R2 to SQL Server 2017 Standard (on Linux)
There is a similar, but not exactly the same, question here:

Azure SQL Data Migration Assistant is Stuck on &quot;Migrate Data&quot;

However, it does explain the limitation you're hitting:


  The Extract service connects to a database, reads all of its objects and their properties, and then creates an in-memory model of the database.


If the database you're trying to migrate has an exceptional number of schema objects, this in-memory DAC model potentially overwhelms the client application / system (Data Migration Assistant running on your PC in this case), resulting in the OutOfMemoryException.

Your next best bet would be to use tried and true approaches like backup / restore in order to migrate to the new machine.