A hand 扌 lifting something by its handle, arm hanging straight. From lifting objects to lifting topics into conversation: raise, mention, propose.
提高 raise/improve, 提问 ask a question, 提醒 remind (lift someone's awareness). 提前 'lift forward in time' = ahead of schedule — the phrase every Chinese planner lives by.
A HAND LIFTS the bag — and lifts the topic into the room.
提 is how you carry a briefcase in Chinese (提包) — always by the handle, arm straight down. Carrying on the shoulder is a different verb entirely.