Fix an issue where the Publish sheet is not dismissed after published

[crazytonyli]

Description

To reproduce the issue: On the custom post list, go to the Drafts tab, tap the More button -> Publish, tap the "Publish" button or "Schedule" button, and wait.

[dangermattic]

	1 Warning
⚠️	This PR is assigned to the milestone 26.8. The due date for this milestone has already passed. Please assign it to a milestone with a later deadline or check whether the release for this milestone has already been finished.

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[sonarqubecloud]

Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud

[wpmobilebot]

📲 You can test the changes from this Pull Request in WordPress by scanning the QR code below to install the corresponding build.

	App Name	WordPress
	Configuration	Release-Alpha
	Build Number	31546
	Version	PR #25394
	Bundle ID	org.wordpress.alpha
	Commit	5860049
	Installation URL	5ei7sb9bfcg90

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[wpmobilebot]

📲 You can test the changes from this Pull Request in Jetpack by scanning the QR code below to install the corresponding build.

	App Name	Jetpack
	Configuration	Release-Alpha
	Build Number	31546
	Version	PR #25394
	Bundle ID	com.jetpack.alpha
	Commit	5860049
	Installation URL	59kk1kmg9g6m8

Automatticians: You can use our internal self-serve MC tool to give yourself access to those builds if needed.

[wpmobilebot]

🤖 Build Failure Analysis

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[kean]

I think it's good, but please make sure to test all the possible scenarios. I remember struggling with this quite a bit in the prod version.