Windows 10 activation using Windows 7 key

Back in 2010, I purchased a standalone retail copy of Windows 7 for my self-built desktop. I purchased an upgrade to 8.1 in 2014 and then availed of the free upgrade to 10 back in 2015/2016. I sold the desktop last year. Over the course of the 10 years or so, I had a number of hardware upgrades and can recall needing to reactivate Windows on at least two occasions (pretty sure both involved motherboard upgrades). I would have reinstalled Windows at various points, but pretty sure I didn't need to enter an activation code.

Before selling the desktop, I should have deactivated the license, but I didn't. Instead, I unlinked the desktop from my list of devices in my Windows live account, thinking that was the same thing. Silly mistake; just didn't do my research.

Fast forward to this year and I purchased a new laptop without a Windows license, as I had intended on using my previously purchased copy. My 25 character key from the original Windows 7 box didn't work. After looking through my emails, I couldn't find any record of an activation key from my 8.1 or 10 upgrades. Got on to Microsoft support and after dealing with 3 agents, they verified my original 25 character activation code was valid, but that the Windows 10 upgrade would have only been valid for the hardware that the upgrade took place on. I was surprised by this as one of my aforementioned reactivations of Windows was definitely done while using Windows 10.

As far as I'm concerned, I have paid for a retail copy of Windows that has been upgraded to Windows 10, but Microsoft are sort of telling me I can't use it any more. Does anyone know if this agent is actually correct and/or if I have any way of activating Windows 10 on my new laptop without having to purchase it again? I have thought about installing Windows 7/8.1 so see if I can activate it this way, and then upgrade to 10, but it seems like a load of hassle for something that probably won't even work.