Rerender cell toolbar button upon cell execution

I have a cell toolbar that isVisible depends on whether the cell has an error. All this works fine. If I click on a cell with an error the button shows up and vice versa. However, if the cell is executed while the active cell remains the same, the cell toolbar is not rerendered hence the isVisible check does not execute. So if I have a cell and I execute it with Ctrl-Enter, if there is an error, the button would not appear after the execution, I’ll have to click away and click back to the cell to have it appear.

Is there a way to rerender the cell toolbar (or just the specific button)? How would I even access it given the Cell object? Or is there some other solution to my problem?