Started this this help article which is written for V8i and not CONNECT but believe I've added the line styles to the seed. Drew lines set to the appropriate layer and the line styles are correct. Seed is in a ProjectWise workspace and exported for use with FME:
Workbench clip:
DGN Styler configuration:
DGN writer:
Translated DGN shows the correct line style in properties but not in the display:
Re-importing line styles warns of duplicates:
But afterwards the line style is correct: