What does autogrow run in the background (Is it a DDL statement?)
As documented by By Parikshit Savjani in
Insert bulk failed due to a schema change of the target table:

This error says that there have been changes in the schema that require the re-compilation of the plan and Insert bulk cannot support recompiles.
Any Operation on the Target tables which would require the recompilation of the query will cause this error messages.
In a normal scenario, the Schema Change could be addressed by a re-compile, however it turns out that for BCP re-compiles are not possible because at compile time, we are reading metadata from the input stream and we set up our statement based on that, and then basically discard that metadata. If we recompile, that metadata is completely lost, and compilation is no longer possible.

There is no reason that auto growth of a file would cause a plan recompile.
I would suspect auto statistics update as the most likely option but the link does mention some other possibilities:

Parallel Bulk Inserts happening on the same table, and foreign keys are enabled on the table.

Parallel Online rebuild index operation running.


It also mentions that bulk inserting with the option to ignore constraints will bump the internal metadata version, which can lead to this error. The workaround is to drop the constraints before the bulk operation, then recreate them afterward.
You could turn off autostats for the table using norecompute for the duration of the operation and then update them afterwards.