Big congrats on your second babe!
Sylvia and Vivian do have a 1920s-40s flapper/ girls in the army van celebrating V-E Day feel. I can see them together, and they are strong and full of presence and staying power.
FWIW (little!), I personally don’t warm to the name Vivian - I find it harsh and masculine (being originally a boys’ name). I prefer the French, Vivienne which gives the more “enne” emphasis and feels more feminine and chic, but I get visually Vivian has the repeat letters and look of Sylvia, and I really like tailored names as well.
Are Sylvie and Vivi too close? Probably not, but a small factor.
With Sylvia, and for another powerful name, I might instead choose Delphine, Beatrice, Rosamund (Romy), Rosalind, Tamsin, Celestine, Verity, Gwyneth, Philippa (Pip), Bryony or Imogen (Immy), Leonor etc.
But assuming going with Vivian, how about:
Vivian Margot Eloise
Vivian Rosalind Faye
Vivian Lucy Delphine
Vivian Chloe Estelle
Vivian Aurelia Maren
Vivian Poppy Mabel
Vivian Zara Lucette
Vivan Esmé Claire
Vivian Tabitha Louise
Vivan Hazel Blythe
Vivian Mary Christine