Can someone help me understand how to activate Office 2019 on my second PC (laptop)?

I built a new Desktop/Gaming PC last summer (Win10 Pro) and installed Office 2019 and bought a legitimate Office key from someone a friend recommended and registered/activated it. All good there, works great.

About 2 months ago I started having issues (RAM went bad) with my 2nd PC/laptop. So, I backed it up, installed a new SSD, replaced/upgraded the RAM, and installed a fresh copy of Win10 Home. I also wanted to install a new version of Office to match the same version I had installed on my Desktop. I installed Office 2019 and went to Activate it and it's telling me that "This account doesn't have Office yet. Office isn't associated with MyEmail.Outlook.com account. To use Office, select one of the options below: Buy / Use a different account / I have a product key".
So I entered the new Product Key I just purchased and receive this message: "Please double-check your product key and try again. We're having trouble recognizing it. Error: PIN-INAPP-INVALIDPIN-8".

Please confirm, I do need a second Product-key, correct? Or is the activation somehow keyed off of my Outlook.com account?
(I thought I read on the internet that I can activate multiple (up to 3 copies) with a single license. I tried that and went through the whole phone activation, using my old key from last year and it tells me it's not valid and to get another one (?? it's active on my desktop PC)

If there's a problem with the key, I will reach out to the guy I purchased them from, he told me to contact him if I had any issues.