"A sea is a large area of salty water that is part of an ocean or is surrounded by land."
It's a basic truth of language that words mean what they are widely used to mean. If it's called the Caspian Sea then it is a sea. By all means exclude it from the definition of "landlocked", but don't pretend it's not a sea.
You are quoting the definition of sea as a countable noun [Collins] or a part of a name (Caspian, Aral, etc.)[Oxford]. The fact that you didn't went for Oxford or Webster and then specifically picked third definition from the Collins webpage, instead of the first one like a normal person would, makes me think that it was a deliberate attempt to sound smart. Or, at the very least, a clear case of confirmation bias, where you tried to find a definition that fit your opinion, rather that the truth. The true definition of the word is:
"The sea is the salty water that covers about three-quarters of the Earth's surface."
That definition is not really helpfull in this matter, so I would rather use the one from Oxford dictionary, as Oxford is usually the "go to" anyways:
"the salt water that covers most of the earth’s surface and surrounds its continents and islands"
A country with an area of over two million square km, with a coastline that's about half the length of the Panama canal.