I used to work in this field in the local authority and although I am a few years out of touch, on my watch this would have be passed for a safeguarding investigation, and notified to the OPG and also to the police who would decide whether it was theft or not.
What would play into that is whether your mother was deemed to have capacity at the time the "gifts" were made. A large factor will be whether the POA was registered at that time. If it was not registered it will be viewed as your mum's decision - but coercive control could be considered.
If POA was registered then it may well be considered financial abuse.
Also they will look at her previous pattern of giving gifts. It is amazing the number of people who get POA registered and then unilaterally decide what their parent would REALLY have wanted was to give everyone in the family lots of money or to pay for holidays or university education.
If it is decided that she intentionally deprived herself of assets, the local authority can assess her as if she still has the money that she gave away. That means that they can make the decision to not fund her care until she reaches the point in time where her money should have run out if the gifts were not made. The care home will want to be paid so they absolutely can give notice. The family may have to pay the money back to enable her to stay there.
If not, then she can be placed in another, cheaper home. The upheaval of a move for someone with dementia should not be underestimated.
Depending on whether you also signed off on this i.e. whether it was joint POA not joint and several POA, you could be implicated. You have no choice but to report this to OPG.
If you do not, then in a few months time the local authority will be investigating and reporting it.
Basically, it will be investigated and probably by several agencies.
If your mum did it intentionally the local authority can decide not to fund her until the time she SHOULD have reached the threshold.
If your sister did it, your sister is potentially facing criminal charges.