This is as I understand it.
Each locomotive knows it's own ID. So you can take it from layout to layout and it will always respond to the ID you set it to, even if there is another locomotive with the same ID on the layout.
The information you see on the Legacy Cab-2 remote display is stored in the Legacy base. So you can take your remote to a different layout and it will then show what is in that base, not your base.
So as for your locomotives, the IDs are all stored in the locomotives, regardless of what the display shows on the remote, the only thing the base has is the info shown on the screen of the Cab-2 remote.
If you have the Cab-1L base and remote, then AFAIK there is no info stored in that base, it is the same as the old TMCC base, which also did not store any info. You can do all the remote swapping you want and not worry about anything.