I decided to check with ChatGPT. Some of these are obvious, but others I never would have made the connection:
Nautical Phrases Still in Use Today

A clean bill of health
Origin: Ships had to have a “clean bill of health” from port authorities, certifying no contagious disease on board.

Above board
Origin: Goods kept “above board” (on deck) were not being smuggled.

All hands on deck
Origin: A call for all crew members to come to the deck and be ready for action.

Batten down the hatches
Origin: Securing the ship’s hatches with wooden battens before rough seas.

Between the devil and the deep blue sea
Origin: “The devil” was a seam in the hull of a wooden ship. Working on it meant being close to falling into the sea.

By and large
Origin: A sailing term describing a ship that sails well in both favorable ("by") and unfavorable ("large") winds.

Close quarters
Origin: Originally a term for a barricade used in shipboard fighting, now used to mean confined space.

Cut and run
Origin: To cut the anchor line and make a quick escape.

Feeling blue
Origin: A ship would fly blue flags and have a blue band painted along her hull when a captain or officer died.

Hand over fist
Origin: Refers to pulling on a rope quickly and efficiently, now means making rapid progress (often with money).

Hard and fast
Origin: A ship that was beached or stuck was “hard and fast.” Now means fixed or unchangeable.

High and dry
Origin: A ship stranded out of the water, now means abandoned or in a helpless situation.

Know the ropes
Origin: Sailors had to learn the rigging (ropes) of a ship; now means someone is experienced.

Loose cannon
Origin: An unsecured cannon on a ship could cause massive damage. Now refers to an unpredictable person.

No room to swing a cat
Origin: Refers to the cat-o’-nine-tails used for punishment—tight ship quarters made it hard to use.

Over a barrel
Origin: A drowning sailor might be placed over a barrel to expel water from their lungs. Later used for flogging too.

Pipe down
Origin: The boatswain’s pipe signaled the end of the day—crew had to be quiet.

Shipshape
Origin: Ships had to be kept orderly and tidy; now used to describe something neat and in good condition.

Show one’s true colors
Origin: Warships would sometimes hide their flags until battle. Showing true colors revealed true intent.

Three sheets to the wind
Origin: Refers to lines (sheets) that control sails—if loose, the ship would reel like a drunk person