You would probably start with a salt marsh with light vegetation as the river feeding it dried up. Then the ground near to where the river came in would dry up leaving soil which would initially be salty but eventually would change and then more vegetation would grow on it. That vegeation would either stay pretty scrubby or turn into trees depending on how much water flow or rainfall you could get to the soil. But in essence it would turn into a normal bit of coast line alththough it would probably have an odd undulating shape to it until over time it would flatten. Either that or the land would erode back, or deposit sediments from the sea pushing the sea out depending on the sea currents. In which case the ground left behind would be a low land plain or level.

In the case in my local region of Glastonbury, Somerset, and Avalon which is part of the Somerset Levels where this has happened in actual fact the sea has come in and out several times in the last few 10,000 years and the situation is quite complex due to ice ages and thawing and changing sea levels. Around 2-3 thousand years ago it was at a stage where it was a brackish water logged plain but humans then got involved and cut channels into it to dry it up for farming. Now, large areas of it still floods in winter where farmers expect it, and abandon those fields to the water, and then almost all of it is dry in summer where its generally grass quickly shoots up and cattle put out in the summer. Somerset is called that for being the Summer Isles as the ancient people came in during the somer months only and the early name of Glastonbury in old Welsh (which predates the Latin from the Roman invasion) means the Isle of Glass because it is said that in winter the lands flood and then freeze over so its and island amongst the frozen glassy plains. So lots could go on in a place like that and the exact circumstances would drive what happens. It wouldn't be difficult to make a claim for quite a variety of outcomes for it. Geologically, 10,000 years is not a lot and things will settle down and the land will eventually go one way or the other.