Lufthansa: When To Escalate EC261 Claim To SOP?

My original LH flights from San Francisco to Frankfurt to Zagreb (LH 455 and LH 1404) on April 13 were canceled. I was rebooked for the same flights on April 15. That was canceled. I filed my EC261 claims on April 19 and gotten confirmation they had received them that day along with claim numbers.

On June 9, I received an email from Lufthansa saying they were still working on my claim.

ChatGPT recommended I send a follow-up email to customer.relations@lufthansa.com asking for the status. I did that on June 15. ChatGPT then suggested waiting until the first week of July to escalate to the SOP if my claim wasn't completed and paid.

Should I ignore ChatGPT and escalate now?