tiles, and can prove that this is the optimal solution.
The semi-invariant we need to track is the score $X$ of pairs of adjacent squares where one is gold and one is not. Initially, $X$ is at most eight times the number of golden squares, which is $100$ in this puzzle, so $X \leq 800$, and because of how golden squares propagate the score will never increase over time.
Observe that $X$ is always even, because $X=0$ with zero golden squares and $X$ always changes by an even amount if you turn any square golden. Also note that if $X=800$ in the beginning, then the score will decrease at least once within the next four days unless the pattern stabilizes before that time. We can safely assume that the optimal pattern takes more than four days to stabilize, so we know that $X\leq 798$ by the time it does.
We are now looking for the largest possible pattern with score at most $798$. A short computer search determines that one such pattern is the octagon obtained by starting with an $86 \times 85$ rectangle and cutting off four equal triangular corners with $28$ grid squares to a side. This octagon has an area of $5686$ grid squares.
Finally, we must find an initial configuration of at most $100$ golden squares that ends up filling this entire octagon. A bit of manual experimentation in Golly lets us obtain such a configuration:
Aside: Finding this by hand was trickier than expected, since it is surprisingly difficult to reach all sides at once without losing any score at any time. I'm sure there are prettier solutions.
Golly 4.0+ pastable RLE of this solution:
x = 86, y = 85, rule = B45678/S012345678History