@nancyeab I work in a non-profit and we have the same language. Luckily I’m in a state with partially-paid disability and family leave.
Non-profits can be weird places with a different work structure. If you’re comfortable, you could ask your director for a meeting and ask if there’s and possibility for change in the manual.
You may also be able to appeal to your board for a partially or fully paid leave of absence.
Good luck!