How to Keep IME Open When Using Buttons for Input in a Custom Japanese Virtual Keyboard in WPF?

Question

I'm developing a .NET WPF application, and my client requires a custom Japanese input keyboard.
The input method is not through a physical keyboard but via UI buttons that input each character.

Here is my problem: when I use mouse to press a UI button, I want the IME (Input Method Editor) to appear with candidate options and dynamically change based on the button clicks, similar to keyboard input. However, every time I click a button, the IME closes, which disrupts the input context.

I tried handling input by restricting button events, but it didn't work.
How can I keep the IME open and maintain the input context when clicking buttons? Any suggestions or workarounds would be greatly appreciated.
Thank you!