However, as soon as you switch on track changes every comment ever made in the source document is still there in the target.
Yeah, comments will be preserved, but you can delete all comments in one step from the Review tab. The details depend on whether you want to keep some comments in the target document or not.
If you have existing comments that you want to keep in the target document, add an "intermediate" step as follows: Copy the content into a new, blank document first, delete the comments (Review tab > Comments group > Delete > Delete All Comments in Document) and then select, copy and paste into the final destination.
Remember that if there is markup (Deletions, Insertions, etc.) in the text, the rules from https://shaunakelly.com/word/sharing/howtrackchangesworks.html#HowToCopyTextContainingTrackedChanges will apply.