I beleive that Labour see this new ID system as the solution to all the age verification questions now required by the Online Safety Act. e.g. access to things like Reddit, BlueSky messaging, Spotify.
With that in mind I think new data you're talking about will be enhanced tracking and monitoring on everyday online activity of UK citizens.
I honestly understand the problem with immigration, but at the same time, I think this way of approaching the problem is just to create "the enemy" from 1984.
It seems that immigrants right now move something between 4B-10B a month in UK which is not a small number. Considering the costs elsewhere altogether, it seems quite small win for the risk.
This ignores the fact that most of Europe and Asia already have national IDs