How much room can you get for $2,000 a month in SF?
At $2,000 a month, a private room with stronger amenities and a more central location may be available, depending on timing and neighborhood. It is still shared housing, so the lease and household matter as much as the square footage.
Use the added budget to reduce daily friction: a short commute, good light, reliable heat, usable workspace, laundry, or a household with fewer people. Decide which of those would make the biggest difference after the novelty wears off.
Do not let a high asking rent excuse weak terms. Confirm utility costs, deposit handling, parking, guest rules, and whether rent may increase. See the actual room, not only a similar unit or an old photo.
The best use of a higher budget is peace of mind: a room you can stay in without needing another search in three months.