When To Escalate EC261 Claim To SOP For April Strikes?

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?