Re: "Cannot drag Voice Control window to a fixed corner in macOS"
Am no expert in this area, yet your post to us certainly deserves some response.
In the absence of any replies to your query ... here's what I found that may be helpful.
Try clicking on the small Voice Control microphone icon to "hold and drag" it anywhere you want before releasing it.
See how to Use Voice Control commands to interact with your Mac - Apple Support
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Apple Support's article below provides some commands for moving or resizing windows, although am sorry to say this uses VoiceOver rather than Voice Control
VoiceOver interaction commands on Mac - Apple Support
Eg: says:
"VO represents the VoiceOver modifier that you press with additional keys to enter VoiceOver commands. By default, you can press Control and Option together or just press Caps Lock".
"Move a window
VO-Accent (also called Grave Accent)
Then use the VO and arrow keys (for example, press VO-Left Arrow to move a window left). To move a window diagonally, use the VO and two arrow keys (for example, press VO-Left Arrow-Up Arrow to move a window diagonally left and up)."
"Resize a window
VO-Tilde
From the menu, choose Resize, Resize and Move to Grid, or Resize and Move to Section. Then navigate to a submenu where you can choose to resize an edge or corner, resize and move to an area of a grid (such as the top left), or resize and move to a section (such as the bottom half).
To resize an edge, use the VO and arrow keys (for example, press VO-Right Arrow to extend the right edge of a window).
To resize a corner, use the VO and two arrow keys (for example, press VO-Right Arrow-Up Arrow to extend the top-right corner of a window)."
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More info: Use VoiceOver to move and resize items on Mac - Apple Support
Eg: says:
"You can use certain number keys to quickly move windows and objects around the screen: the top (left, middle, and right) section using keys 1, 2, and 3; the centre (left, middle, and right) section using keys 4, 5, and 6; and the bottom (left, middle, and right) section using keys 7, 8, and 9."