The lineages in Van Richten's Guide (Dhampir, Hexblood and Reborn) all can now carry over certain aspects of their race (Swimming and Climbing speeds as well as any proficiencies). What I am curious about is if the Variant Human's free feat would also carry over into one of the lineages. It doesn't specifically say if does or not, and so I'm left confused as to how it works.
Nothing carries over from your former race, except those things explicitly named in your new racial features.
The rules for lineages state:
If you choose a lineage, you might have once been a member of another race, but you aren’t any longer. You now possess only your lineage’s racial traits.
Each lineage has the trait Ancestral Legacy:
If you replace a race with this lineage, you can keep the following elements of that race: any skill proficiencies you gained from it and any climbing, flying, or swimming speed you gained from it.
Since the feat from Variant Human is none of these things, it is not retained.
This makes sense, as a full array of racial features plus a feat would be totally broken.
The lineages represent a full array of racial features. The Variant Human doesn't get any racial features besides a single skill and +1 to two ability scores. Giving a character a full feat on top of the racial features of a lineage would be extremely unbalanced.