EC 261/2004 applies because this was a departure from the EU and the delay was not caused by an extraordinary circumstance, e.g., it was either an error by CX or a CX contractor.

The dispute will be whether this was a 30-minute delay at HKG which would not result in any compensation for any Type flight or a 7-hour delay at PEN, your final ticketed destination, which would result in EUR 600 cancellation/delay compensation for a Type 3 flight.

The law seems settled if the first segment were within the EU, but there remains dispute on the current situation. But, it will be resolved soon enough.

Make a claim with CX. Be very specific that it is for EUR 600 and that this is because the delay is measured by time of arrival at PEN as your final ticketed destination. Keep the complaint simple and short. Leave out extraneous details.

Your claim will almost certainly be denied. It is always possible that CX offers you something. You are always free to accept what is offered. Only you know the value of your time. If you do, you are done. If you don't, proceed as below.

Presuming that you are UK-based, you have access to MCOL. If not, you still have access to the small claims process and its telephone hearings. The forms for a Letter Before Action are on the MCOL website. Use those either way. File in short order and maybe CX will pay just to get this done, maybe it will fight and maybe it will offer more than before. Compromise is always up to you.