POA procedure; how does the appointed agent get informed of their status?

I agree. In my instance, I went with my Mom to have her make up a new will after Dads death. While there, we did her POA where I was assign ed agent. I signed nothing. So, yes you could be made POA without your knowledge. So if the person doesn't tell you and give you the original paperwork you may never know. It is not required for POAs or Wills to be recorded with the county. Which I think they should be.

In my experience (US) it is absolutely possible for the agent NOT to know they have been appointed by the principal. The agent is not required to sign, only the principal assigning the power signs before a notary of the public.
And no, the law office would not be required to communicate with the agent.
I suppose the principal could request that the attorney take that on but it’s not a given.
If I were you I would check the laws for the state you live in as I have seen some deviation mentioned on this site.
The wording of the POA is important as some give powers others don’t.
Also know that the principal can change their mind and appoint another as long as they are competent to do so. They don’t need the permission of the existing agent.
So, the principal would need to inform the agent.

In Canada, but my experience.

First you have to agree to be POA. Second you have to sign off on the paperwork, but you do not have to be present when the POA is drawn up. However your signature may have to be notarized. My brother and I are POA for Mum, me first he is the second. Three copies of the POA were created, we had to sign all three copies plus the original. We each have a copy, the original is at the lawyer's office.

Mum recently had to 'Spring' stepdad's financial POA and Representative Agreement (Healthcare POA in BC). She called the lawyer, who created a new document for Mum to take to the banks for the financial POA and the Healthcare document to be filed at the hospital.