You usually do not need a reply to a thank-you message for the interaction to have been successful.

A thank-you note often closes the immediate conversation. Another message should have a new reason, not simply ask whether they saw it.

Reconnect later with a relevant update, recruiting milestone, or specific question if there is a genuine reason.

Avoid sending a second thank-you or a message whose only purpose is to get acknowledgment.

My cover letters got better once I stopped trying to mention every achievement and focused on the logic of the move.

For final rounds especially, I think calm delivery matters as much as the exact wording.

I would ask one clarifying question only if it changes the decision. Too many can sound like you are avoiding a view.