The Vanity Fair article contains quite a few of speculations. One of them was
In addition, Andrew will reportedly not be invited to any of the public ceremonies honoring his father, Prince Philip, on his 100th birthday next June.
This was apparently based on The Sun, where "an insider" mentioned that "He will not be invited to major celebrations and organisers have been told to avoid pictures of him in a photo exhibition." The photo exhibition will be organised by the Royal Collection Trust.
https://www.thesun.co.uk/news/12654179/prince-andrew-philip-100th-birthday-airbrushed/
I don't understand why Vanity Fair have to drag Andrew's name in Princess Eugenie and Jack Brooksbank's future children arrangement. This is especially with a very unreliable source on Prince Philip's 100th Birthday arrangement. Ok, Baby Brooksbank might be included in the "photo exhibition", but nothing is set in stone.
The VF article also mentioned about the absence of official photograph of Savannah Phillips, Isla Phillips and Mia Tindall, after their birth. Archie did have an official "photo-call and family portrait" after his birth, as well as "official portraits" after his christening.
The public events surrounding royal births have varied over the last decade. When Prince Harry and Meghan Markle had their son, Archie, his birth was followed by an official photo-call and family portraits. While his christening was held privately, a series of official portraits were released a few days later. For the Queen's grandchildren without titles, the affairs are much quieter. When Peter Phillips’ daughters, Savannah and Isla, are the queen’s two oldest great-grandchildren, were born in 2010 and 2012 respectively, the palace released statements, but no official photos accompanied them. Their christenings were also private, though the queen was in attendance. When another great-grandchild, Mia Tindall, was christened, the public only saw pictures of the family assembling because an ITV reporter just so happened to be visiting the Gloucestershire village where the ceremony took place.
Of course the photographs will depend on the location/time of Baby Brooksbank's birth and whether or not Eugenie and Jack or the Royal Family want to release pictures (alongside with the announcement). I am not quite sure when the York Princesses usually leave Sandringham Estate after Christmas. Otherwise, I think Eugenie could give birth in Sandringham, rather than London if the expected date is very early 2021. There is also the possibility of releasing photographs after Baby Brooksbank's christening.