"Insufficient access: insufficient access rights on object id:[0031a...]"
When trying to sync the Salesforce record, an error is thrown "insufficient access right to object ID [..]"
This error is usually related to the integration user not having enough access to the object as mentioned in this Salesforce knowledge base.
In Salesforce, it is recommended to make sure that the integration user is allowed to "modify all" objects.
Go to Setup > Administer > Jira Cloud/Server for Salesforce > User Count (click on the number).
Click on the profile and find Standard Object Permissions or Custom Object Permission depending on the object that's causing the issue.
If you are unable to search for the profile from Step 2, use this Salesforce guide alternatively.
Click Edit and grant Modify All permission to the profile.