They've always been able to conduct those searches, it's now in the guidance to inform some police officers (men) that they exist.
For those that are interested, here's the guidance
https://library.college.police.uk/docs/NPCC/Practice-advice-child-death-investigation-2024.pdf
From looking at that, a certain level of investigation will be started where there is an unattended stillbirth (not miscarriage), but given that there'd almost always be some form of labour at 24+ weeks, which would result in the woman going to hospital or phoning an ambulance, there can't be many in this category. Other cases that may be investigated are those with suspicious circumstances, just as before this guidance. None of this investigation necessarily entails searching the woman's house!
No one is pushing for routinely searching womens belongings after a stillbirth in this country. But if (hypothetically) a woman tries, for example, to obtain an abortion out of time by lying about her dates, then tells her midwife she'll 'do whatever is necessary' and then 3 days later phones up because she's had an unexpected stillbirth at 30 weeks out of the blue, yes, the police might look into it. Just like they would have before.
Equally, don't discount the situation where an abusive partner induces a stillbirth, either by using abortion drugs or by violence.