The reason it "cost" so much is because it was never used. You have confused stack with a flow. Basic error. In addition, the expectation was that it would be a deterrent because people are coming here primarily for economic reasons. The reason the government believed this to be the case is because the same thing has been tried in other countries and worked, Australia did this and now (in a turn of events that will presumably shock you) people are complaining that the cost of the deterrent is too large...because no-one tries to get there by boat anymore.
We have to find temporary accommodation anyway. Rwanda changed absolutely nothing about that policy, I am not sure how anyone could think otherwise. It is enshrined in our law functionally: if someone comes here illegally, we have to house them in a hotel and then we have to provide them with a council house if their claim is successful.
One of the bills, theoretically, created the legal basis to detain anyone who comes to the UK by irregular means. However, and despite the usual noisy crowd saying it was the end of democracy, there is no functional capacity within the Home Office to effectuate this...quite simply, there is isn't the administrative capacity (or, with Labour, the political will). This power exists and is completely unused. We are also unable to return people which makes indefinite detention of 300-400k people at a minimum challenging.
But this act is used to detain some illegal migrants in prison in some cases. Usually this is terrorism-related but, I believe, this has also been used in the many cases of sexual assault.
It was not illegal to process claims whilst the Rwanda scheme was running. One, it was never started, it was due to start after the last election if the Tories ran. Two, it did not change the status of people arriving, the Tories put substantial resources into the Home Office to reduce the backlog (one of the issues here is productivity because so many claims are accepted and there is a large industry dedicated to helping claimants, average processing time is 14 days...it is very slow).
Labour policy is to create a wedge because, to be frank, reducing immigration is devastating for a party that relies so heavily on voters who feel a kinship with the vast majority of illegal migrants. In some areas, Labour majority is almost all this demographic, and almost all illegal migrants make up this same demographic. We are speeding down the path to balkanization, this happened under the last Labour government and has happened under this one. There is a long historical record here of this happening in other countries that people are determined to ignore. One of the reasons why Labour went for student visas immediately, in addition to the massive level of fraud, is because people from these countries do not vote for Labour in the UK. Leaving Pakistan off the list, when it is a country that also does not accept returns and has huge number of fraudulent student visa was very obvious (and btw, some UK unis no longer accept students from Pakistant because of the fraud...this is exceptional). That is the wedge.