When we did my DM's POA we didn't have to get an assessment of capacity, but I don't know whether that is because she doesn't have any mental capacity issues.
You do need someone to sign that they are happy that your Gran understands, at the time of signing, what the POA form is. We used a neighbour of my DM's for this, think you need someone who has known them for over 2 years, and isn't related to any other party, or you can use a professional eg solicitor, GP, social worker, but there will probably be a cost to use them.
We tried to get POA for my DF when he was diagnosed with terminal cancer last year, but his mental capacity deteriorated so rapidly that we missed the boat.
We arranged a POA for my DM even though she is in good health as not having one for my DF just added stress to what was already a stressful situation. We registered the POA immediately and have set it up so we can use it straight after it has been approved, in case we ever need to.
A finance one is important because a bank can freeze a person's account once they are aware they have diminished mental capacity, and therefore there would be problems paying for care etc