Atlassian requires all integrations with Jira Cloud to use API tokens rather than passwords for authentication. Attempting to use a password for authentication will cause a 403 error when attempting to send or receive updates between Aha! and Jira. You can follow these instructions to ensure you are using a valid API token when configuring your Jira integration.
Multiple servers resulting in 403 authentication errors
The Jira via Connect integration uses an Add-on that is installed into your Jira instance by an administrator and can only be used with Jira Cloud. This Add-on only supports integration with a single server meaning it can only be associated with your Aha! account and one Jira instance. This is different from standard Jira which supports integrating with multiple servers.
The danger is nothing prevents you from setting up integrations with multiple servers through the Connect Add-on. When doing so it will commonly result in integration communication issues when trying to perform an update Jira action as the wrong Jira server is used resulting in a 403 authentication error message.