Fix CMM-940: Allow accessing Jetpack sites without the jetpack plugin

[crazytonyli]

Description

Fixes https://linear.app/a8c/issue/CMM-940.

Testing instructions

Verify CMM-940 is fixed. There are steps to reproduce the bug in the Linear issue.

[dangermattic]

	1 Warning
⚠️	This PR is assigned to the milestone 26.5. 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.

Generated by 🚫 Danger

[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	29729
	Version	PR #24976
	Bundle ID	com.jetpack.alpha
	Commit	c7a4722
	Installation URL	2bthaos0f0mp0

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

[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	29729
	Version	PR #24976
	Bundle ID	org.wordpress.alpha
	Commit	c7a4722
	Installation URL	2co8vvudnd438

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

[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