In the main thread for this topic, in the Coronavirus forum for UK Arrivals, you will find a long discussion about this. The summary, of a summary, is that the law does require you to book (but not necessarily take) a day2 test. In practice, if you are bona fide in transit and that is the sole reason for your presence in the UK, then the Border Force will be ok with no day2 test. However it's mainly the airlines that check this, not so much Border Force. So particularly if there are separate reservations it may be that the airline will regard you as having a visit to the UK and therefore would want the PLF and day2 to be filled for this.

A stay over 24 hours is a not a flight connection - that's unrelated to all of this - so connecting baggage won't be through checked. If this is a big factor then it's better to have a sub 24 hour connection, which also makes it easier with the testing issues too. On the other hand, it may be best for all concerned to get tested at that point since knowing your COVID status is generally better than not knowing it. It could save your life.

LAMP, PCR and LFD will all be allowed from 24 October, they do have to be via an approved supplier and LFDs will need a photo to be sent in to the supplier. More details in the main thread.