Peek: Space triggers Peek while renaming after toggling Peek switch off and on

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### Microsoft PowerToys version

0.100.2

### Installation method

PowerToys auto-update

### Area(s) with issue?

Peek

### Steps to reproduce

After further testing, I found that pressing the Space bar during rename can consistently trigger Peek after **toggling the Peek switch off and back on**.
I noticed there was previously a reported issue where using a Chinese input method during rename would accidentally trigger Peek on Space press. That issue was likely misattributed to the input method — based on my testing, it appears to be caused by the same underlying problem related to toggling the Peek feature switch.
Additionally, after a system restart, pressing Space during rename may also trigger Peek if Peek has not been manually toggled on beforehand.

### ✔️ Expected Behavior

Please test, verify and repair it.

### ❌ Actual Behavior

_No response_

### Upload Bug Report ZIP-file

_No response_

### Additional Information

Windows11 25H2

### Other Software

_No response_

No files or tests are named. First reproduce the issue on Windows 11 by renaming an item, pressing Space, and toggling Peek off and on or restarting; trace the Peek switch and rename key handling, then confirm Space no longer opens Peek and add regression coverage if the existing test structure supports it.

Written by the indexing model from the issue text.