The builtin IntelliJ settings sync feature does not sync the plugin settings, namely the rules and the list of saved prompts.
Likely related: if you export the settings to a zip, you get something like this (email address obscured):
<application>
<component name="AiPluginSettings">
<option name="gotItToolTipsShown" value="true"/>
<option name="lastLoggedInEmail" value="***@gmail.com"/>
<option name="privacyBannerDismissedByEmail">
<map>
<entry key="***@gmail.com">
<value>
<PrivacyBannerDismissalInfo>
<option name="dismissalType" value="DISMISSED_PERMANENTLY"/>
</PrivacyBannerDismissalInfo>
</value>
</entry>
</map>
</option>
<option name="shortcutNotificationShown" value="true"/>
</component>
</application>
which does not include the information concerning rules and saved prompts.
The builtin IntelliJ settings sync feature does not sync the plugin settings, namely the rules and the list of saved prompts.
Likely related: if you export the settings to a zip, you get something like this (email address obscured):
which does not include the information concerning rules and saved prompts.