Born May 1955 DLA to PIP, or not.

My sister has long-term, severe chronic mental health issues. So getting an ESA review form, and before that was done [mercifully kept in support group after a F2F] - getting notice of her DLA ending, was extremely stressful. She did manage to submit a PIP application inside 2 weeks extra time they wrote to her offering. That was autumn 2019. In Jan her new social worker got a call from DWP for more info and saying they may be able to decide without a F2F but it would be another 4-6 weeks 'due to workload''. Early March she got a letter saying they will leave her on DLA until Sept 2021. No explanation at all. She will be 4 months over her State Pension Age by then.
After all that!
Thought everyone should know what they are getting up to. If anyone has any idea if there is anything detrimental about this that should be challenged, please let me know.
Also our daughter got a letter giving 2 week extension unasked, on the Monday before her form was due in the next weekend. Is this a new thing, how should we see it?
Thanks.

Thank you, As far as I know she has been getting higher rate care but nothing for mobility as she is Ok physically.

Thanks for your reply, but sorry I don't quite get the second part of it. She doesn't need Mobility at all, physically. Are you saying she should push to move from DLA to PIP to allow post-pension age changes just in case her needs become greater? For instance she does not go to new places outside her local area alone, so the PIP descriptor about that could apply.
Thanks, Denby