Zoomit: Fix a issue that after trim, the video can't be saved and we can't start a new recording session (#46034)

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## Summary of the Pull Request

The bug was caused by a resource lifetime issue between the recording
phase and the save/trim phase. After a recording stopped,
StartRecordingAsync moved directly into the save workflow while it was
still holding the temporary recording stream and the active recording
session objects, later file operations in the save flow could fail
against that same file. Once that happened, ZoomIt could end up stuck in
a bad state where the first save did not complete cleanly and subsequent
recording attempts would no longer start until ZoomIt was restarted.



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## PR Checklist
As title
- [ ] Closes: #46006
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issues) -->
- [ ] **Communication:** I've discussed this with core contributors
already. If the work hasn't been agreed, this work might be rejected
- [ ] **Tests:** Added/updated and all pass
- [ ] **Localization:** All end-user-facing strings can be localized
- [ ] **Dev docs:** Added/updated
- [ ] **New binaries:** Added on the required places
- [ ] [JSON for
signing](https://github.com/microsoft/PowerToys/blob/main/.pipelines/ESRPSigning_core.json)
for new binaries
- [ ] [WXS for
installer](https://github.com/microsoft/PowerToys/blob/main/installer/PowerToysSetup/Product.wxs)
for new binaries and localization folder
- [ ] [YML for CI
pipeline](https://github.com/microsoft/PowerToys/blob/main/.pipelines/ci/templates/build-powertoys-steps.yml)
for new test projects
- [ ] [YML for signed
pipeline](https://github.com/microsoft/PowerToys/blob/main/.pipelines/release.yml)
- [ ] **Documentation updated:** If checked, please file a pull request
on [our docs
repo](https://github.com/MicrosoftDocs/windows-uwp/tree/docs/hub/powertoys)
and link it here: #xxx

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## Detailed Description of the Pull Request / Additional comments

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wherever possible, but list manual validation steps taken as well -->
## Validation Steps Performed
Validated locally recording works fine when trimmed