She left everything to charity, but looking at the state of the house, there's only the house to inherit anyway. Lady Denham has spent her money, poorly on Sanditon. They've been out of money for weeks with the workers, she is house rich but cash poor. Esther won't need the money anyway if she gets with Babington.
Sidney is not rich. He was dumped for lack of money and he hasn't been able to shore up Sanditon either. As the younger brother of 3? brothers he wouldn't have inherited the family fortune and would only have a yearly stipend. Interestingly, they haven't shown that traditionally the younger brothers would've gone into law or the church.