I have found BAH to be an excellent service especially if things go wrong, first of all.

I believe from the thread that your partner needs to maintain Gold status with a balance of 12990 nTPs (needing 7010 nTPs) so these points are made with that in mind:

1. This year and next we'll get very good bonus nTPs. For F this is 550 nTPs per flight. You'll both get this whether you're purchasing a BAH or not. So for your trip to South Africa you'll both get 1100 nTPs. Total = 14090 needing 5910 nTPs.
2. Since BAHs get split amongst travellers on the booking, you'll need to spend 5910 x 2 = £11880. I suspect you will have no problem doing that with your trip to South Africa in First.
3. You have until April 1st next year to accrue the required number of nTPs - If your partner has a British Airways Premium Plus card then from now you'll get nTPs for spending with this (750 nTPs for hitting £15k, 750nTPs for hitting £20k, 1000 nTPs for hitting £25k by 1st Feb 2026). Again BAH or not.
4. I personally never split booking with my partner. We have had flight and hotel issues on multiple occasions and it would be more of a problem if we were on separate bookings. BAH and BA have always been extremely helpful but there are only so many things they can do if there are flight issues and you are on separate bookings.

So I think you can meet your goal of Gold retention just by purchasing the BAH for both of you on the same booking.

If you are interested in your partner chasing GfL then I recommend your partner pays with a BAPP, looks like you won't have an issue meeting the tier requirements and may even hit them in one go.

You'll need to register for both offers (bonus nTPs from BA and Amex nTPs)