I think the most likely cause of your problem arises from your statement:
What happens is that if a Mac of any sort is linked to a previous or current user, nobody else can sign in with a new Apple ID or with an established Apple ID.
That is well documented. What you need to do is have the "owner" of that Mac either dissociate themselves with that Mac (unlikely in the situation you described), or you abandon any attempt to sign in with your created ID.
If you continue with repeated attempts to sign in, there is a potential risk that the owner may suffer. Anyways, you won't get access.
Ian
Although it's not my laptop, it's been primarily in my possession since the organization bought it. It was, however, loaned out to another member of the organization for a brief period of time, and I suspect they may have created an Apple ID without telling us (this is a guess, based on the fact that, when the laptop was returned to me, the OS had been upgraded to Monterey, and I assume an Apple ID would be needed to upgrade, no?). Unfortunately, this other member is no longer with the organization, and is difficult to get a hold of.
I know that I never created an Apple ID until yesterday.
This is in line with "What to do before selling/giving away a used Mac" before a new user (new Apple ID) can use an Apple device all trace of the previous user must be removed. Accounts like iMessage, iCloud, App Store etc must be signed out, Music needs to be de authorised effectively removing the device from the previous account and generally a complete reinstall of the operating system to original.
So, yes you can create a new Apple ID on any device but you can't use it on another person's device until the above steps are taken.
See;
What to do before you sell, give away, or trade in your Mac
In addition, as a final ID verification, you will be required to provide a "payment method" even though you may not want to buy anything from Apple. How this works in a corporate sense I don't know but at some point you will be required to provide eg. a credit card.
Just to reiterate, this MBP was brand new when the organization bought it, I had it in my possession for the most part, but someone else may have created an Apple ID without letting us know. See my reply to Rod above, thanks.
How did you create the new Apple ID and why didn't you use your old Apple ID if you have one?
I have 2 Apple ID's. The first one I created through iTunes in 2002 maybe and the second one I created when I got my first iPhone (4S) in 2012.
You probably need to signing to iCloud.com to confirm the Apple ID is valid/good. Or if you used an existing Emil address, you might be able to confirm you are the account owner through the email provider.
I created it using the usual steps through System Preferences. This is the first Apple device the organization has used, so there was no (or should not have been an) "old" Apple ID associated with it. To note, I have been using Apple devices for almost 20 years now, and have never encountered this issue before.
So, I've tried logging in through iCloud on the web, but that does not work and I get the same "This Apple ID is not active" notification. I've tried every email address associated with the organization, but none of them are active.
What I don't understand is, why could I successfully create the Apple ID, receive welcome and verification emails from Apple and iCloud, but then be denied access?
Unless I hear back from the old member of the organization, and they confirm that they created an Apple ID and give me the username and password, what are my options here? Call Apple (we don't have Apple Care)? Go to an Apple store? Back up the laptop and do a fresh install?
Thanks for the help, everyone. Of course, any more assistance is welcome.