Gendry is not an acknowledged bastard of Robert where as Jon was acknowledged by Eddard Stark to be his son. From GOT Wiki page:
Gendry is a bastard son of King Robert Baratheon, but is
unacknowledged and unaware of his lineage. Gendry did not receive the
bastard surname used in the Crownlands (Waters) because he was not
openly acknowledged by Robert.
No one in Stormlands knows who Gendry is except retinue of Stannis Baratheon but
Stannis was also killed with his men.
Everyone in North knew Jon ever since he was an infant. Lord Jon Arryn, Lord Stannis Baratheon and Lord Eddard Stark are the notable people who knew about Gendry but
they are all dead.
Therefore it is unlikely that Gendry will make it to throne of the Storm Kings.
But seeing as D&D
crowned Jon despite him being a bastard while in presence of a
trueborn Stark (Sansa)
you can never be sure what they will do next. They did not even bother with Jon issuing an edict of legitimising himself. Cersei will claim Stormlands
as heir of King Tommen Baratheon, be sure of that.
Will the Storm Lords accept this? That is another story. They will most likely side with Daenerys against the Lannisters.
But we have to keep in mind, Gendry has one voice which carries a lot of weight. That voice belongs to Arya Stark of Winterfell. If Arya proclaims Gendry as natural son of Robert and Varys confirms it, there may be a possibility that Daenerys may legitimise Gendry and raise him up as Lord Paramount of Stormlands.
In S08E04, Daenerys actually went through with it and legitimised Gendry as Gendry Baratheon, Lord of Storm's End and Lord Paramount of Stormlands. As it happened, Gendry had become well known at Winterfell thanks to Davos Seaworth's testimony of his parentage so Arya's word wasn't needed at all.
In books, Robert has one acknowledged bastard by Delena Florent who is named Edric Storm. He was ferried to safety across the narrow sea by Davos Seaworth and his colleagues. Robert's eldest daughter Mya is not acknowledged but whole Vale is witness that she was fathered by Robert.