Amazon Q Chat Window appears on top of all other windows

I have the Amazon Q Chat Window included in my stack of normal code windows, as a separate tab. It blocks out all other tool windows, which is not standard behavior.

**Steps to reproduce**
1. Open an Amazon Q Chat window
2. Dock it as one of your code tabs
3. Dock the Properties tool window to the left side, but don't pin it
4. Hover over the Properties tool window

**Expected behavior**
The Properties tool window appears over the Amazon Q Chat tab. You can see this behavior if you have another document tab active.

**Actual Behavior**
The Properties tool window appears behind and completely blocked by the Amazon Q Chat tab. None of the elements in the Amazon Q window are clickable because it isn't actually the foreground window, confirmed by the pointer not changing to the finger and remaining as the arrow.

Repeat this with Output/Error List/etc, which I usually dock as fly-outs to the bottom of the bottom of my VS workspace.

Amazon Q Chat obscuring the Properties tool window.

Standard document window behaving nicely with the Properties tool window. Amazon Q Chat is still open and in the same tab position, it is just not active.

**Development System (please complete the following information):**
- Windows Version: 11 23H2 22631.5624
- Visual Studio Version: 17.13.7
- AWS Toolkit for Visual Studio Version: 1.75.0.0

Start by reproducing the docking behavior in Visual Studio 17.13.7 on Windows 11 with AWS Toolkit 1.75.0.0, following the listed Properties and Output/Error List fly-out steps. Compare Amazon Q Chat with a normal document tab; the work is done when unpinned tool windows appear above the inactive chat tab and remain clickable.

Written by the indexing model from the issue text.