Sorry, but could you outline this "training phase" in terms of what it is, how it relates to the OPs role in the programme she works on, and how long it ought to be. References to any relevant law would be useful.
OP, I'm sorry that you are struggling with your new role, but the extent to which you should be picking up the role is exactly what the employer should be dealing with at this stage. Given that you are still on probation ( not that that has much relevance as terminating got job in the first two years is easy enough) I would generally consider it a positive sign that the manager is using a PIP - if they had no expectation that it might make a difference and help you progress, then they just need to sack you and not go to all the bother of a PIP. Equally, I would expect the manager to check on progress with your mentor / buddy, and to all about areas that you continue to struggle with.
What your manager needs to be doing is identifying for you the areas in which you need to improve, what standards are expected, and how they will work with you to meet those standards. On the face of what you have said they are doing that and are putting support in place to help you achieve that. The problem seems to be more that you aren't managing to do that. It would seem reasonable to expect a fairly good level of independent working from you at 4 months in unless this was advertised as a training role.
Is there possibly an explanation why you aren't remembering things? Stage of life or mental health issues can influence memory, for example, and you do refer to struggling in your teaching capacity; and if you were teaching for 17 years, could menopause symptoms be influencing your performance. These are all legitimate possibilities, and many employers can look at flexibility or adjustments if there is a way of managing such things better.
Equally, being balanced about this, if I employ an admin worker to do a specific role, I expect them to come with the skills required, and by 4-6 months I would not expect them to need very much hand holding in relation to the knowledge required.
I very much doubt that they think you are a waste of their effort - they simply wouldn't have bothered with the PIP if they did. That is a positive, not a negative. Could you perhaps talk to the manager or your buddy about how your are feeling, and ask them for some feedback on what is going better? Or just tell them how you are feeling? You have nothing to lose by having that conversation.