Hi @Emilien BOUCAUD ,
Welcome to Microsoft Q&A Platform. Thanks for posting the query.
I have observed a setting "Allow reading files while uploading" in SFTP as below which is by default set to "False". Hence, this would prevent Azure Data Factory to read the file while it is still getting copied.
I don't have SFTP setup so not able to share any repro for the same. And this would cause failure of copy activity but copy activity can still identify those files that are getting copied. To prevent failures, the approach you mentioned - a filter on LastModifiedDate < Pipeline Trigger time should be enough.
Hope this helps! Please let us know if this does not answer the query and we will be glad to assist further.