Can I fit my old PC hard drive into my new PC just to activate Windows 11?

Years ago I purchased Windows 8.1 OEM for around £100 from ***elsewhere***, then when Windows 11 came along I was able to upgrade to it for free.

Now I've just built a new PC but need to be able to activate windows, I've tried copying the product key etc but no joy.

I've read that OEM versions can't be transferred? but also read that I could link my old PC to a Microsoft account and then it would work?

I was wondering if I just take the hard drive out of the old PC with Windows 10 already on it and then stick it in the new PC - will it then activate on the new PC?