The answer seems to be 284 million rolls.
The question isn't:
"how many rolls do we need so that I have a >50% chance of seeing a streak of length L or longer",
or
"how many rolls do we need so that the expected longest streak is of length L".
The question is:
"we have seen N rolls, what is my chance of seeing a streak of length L or longer?"
Which is kind of the same thing, but in the opposite direction, and apparently much harder to calculate.
Solution for a streak of L = 28, for N rolls, in tab "L = 28". Add rows to increase N. Unfortunately sheets is limited to 400k rows. Perhaps another different program could use my formula to compute the answer for N = 357MM?