Do I have warranty on the ink cartridge?

[Tinezusi]

Hello

First question:
How long do I have warranty on the original ink cartridge C2P05A HP 62XL? And how can I claim the warranty?
What are the next steps?
(Please give me a direct link or an e-mail address and instructions, if this would be the way, I have to go through.)

Second question:
Does an ink cartridge have a serial number? I do not think so. But don't you need a serial number to help me? So what number can I give you? I have not problem with a printer, I have a problem with the ink cartridge.

Please note: I have not an ink Subscription. I have boght the ink in a shop.
And I am from Switzerland.
Please note: The store where I bought the ink has gone bankrupt:
https://www.techmania.ch/de/
So I can not take the warrenty services from this shop. It a German Shop in Switzerland.

Quote from the homepage (translated): "Does my warranty claim expire?
Your warranty claim remains valid. You must register the processing directly with the manufacturer together with your commercial invoice. For ongoing warranty claims, we have informed our service partners that your item should be returned directly to you." (https://www.techmania.ch/de/)"

It's one of this super expensive original HP cartridge. It still has 75% content, but it is defective.

When I go here: https://support.hp.com/ch-de/check-warranty
I have to type in a serial number. What number do I have to type in there? C2P05A HP 62XL does not work.
It looks like I can only check the warranty of devices, but not of ink cartridges. What have I overlooked?

And please do not forget to answer my first question.

If you need it: I still have the order confirmation from this shop.

Would appreciate some helpful help.

Thank you.