Problem with overwriting in "llm chat" line wrapping

In an "llm chat" prompt (single-line input), whenever I reach the last column of the line, the cursor overwrites a single character and starts confusing where the line begins.

In this example, I show the problem by slowly typing "test" at the end of the line and then typing C-u to go back to the beginning of the line. The "e" in test at the end of the line is gone and then the space between the ">" prompt and where I am typing is gone.

Start by reproducing the cursor and line-wrapping behavior in the "llm chat" single-line prompt, including typing at the last column and pressing C-u. Locate the prompt input and terminal-rendering entry points, then verify that characters and spacing remain intact at the boundary and that existing tests still pass.