It is up to the FSA administrator to follow the rules and make sure the costs are properly substantiated. So ultimately, you need to ask them what they will cover and what proof they will require.
I suspect that you will need to submit a claim in March, 2024, and you will only be able to claim the cost of care from 1/3-3/15 (which would be around $2000 of the pro-rated up-front fee, plus the weekly stipend.) However, you can't include any part of the costs that are for housekeeping services, just the child care.
If you can't add up to $5000 of expenses, you may forfeit the balance of the account. And, you would have to upfront the money and then request reimbursement in March, I suspect the plan won't pay you before the care occurs.
If you also have a DCFSA for 2024, you should have no problem getting the full reimbursement for amounts paid from 3/15-12/31.
You don't say if you had other care expenses in 2023, those could also be reimbursed, of course, to get the money out of the account.
Also remember that the au pair only qualifies for the DCFSA treatment if the child care is provided so that you and your spouse can both work, or go to school full time.
Lastly, your 2023 tax return will list the $5000 DCFSA benefit on form 2441. If you have no qualifying expenses for 2023, you will report that you carried forward the entire $5000 to 2024.
