Transferring Non-Purchased Music

I am upgrading my iPhone from an 8 to a 13. The music I have purchased downloaded successfully and all is good there.

However, the music I had downloaded to iTunes from CDs a while back, and then transferred to my 8 did not move across to my 13. When I connect my 8 to my PC and I go into iTunes and look to Sync Music I get the message "Are you sure you want to remove existing music, movies, TV shows and books from this iPhone and Sync with this iTunes library?"

If I click "Remove and Sync" will I lose all of the music from my iPhone? Or will iTunes on my PC and the music on my iPhone really Sync and I'll have all songs in both places?