@nine_tail
The solution to your problem is essentially the same as given in >>this thread<< for an experienced user.
If you could model from scratch something like this image...

... you would have a better understanding of how the original object was created. (The body most likely on a clay pottery wheel.)
Let's review the information you have given:
1. A rough scan (always hard to work with, even for advanced users). Some photos of actual piece would most likely help.
2. The first step you did was to degrade the rough geometry scan you did have into even poorer geometry, but apparently not observe this degradation and ask questions about how to avoid going backwards.
3. Unfortunately, the next few steps you made in attempting to solve the issue would seem to indicate that you have never seen a video of a teapot being turned on a potter's lathe. I doubt this is the case, I assume you have some experience, but it confusing to see the approach that you attempted.
Now, let's make some suppositions in the absence of information.
To me this looks like a broken pottery shard that you do not have any more of the pot.
You would like to fill in part of the area you showed, and that I modeled, so that others can get a visualization of what the pot would have looked like without modeling the entire pot. An archeological example.
If my assumptions are correct, you should have provided this information, photos of the actual piece, and photos of similar archeological presentation pieces that you or someone else already completed similar to what you are trying to accomplish.
If my assumptions are wrong - well you see the issue here - nobody knows what you know about where you are going with this. That information is probably useful. If my assumptions are wrong, then I was already going in the wrong direction.
How much work - how cleanly, do you want to match this to the original shard?
For a very very close match you would have to grind the edge of the original to smooth uniform surface, I assume you do not want to do that.
That would mean that the patching piece is not going to precisely match the edges (as shown in my example), but after printing the patch you could use clay to bind to the original piece. In the past I have used drywall compound to completely cover the 3D Print as it dries relatively quickly and is easy to sand smooth. Of course, you want the patch to be a different color than the original shard to illustrate what is original and what is patched.
Let's start by filling in the missing blanks of information on the true Design Intent on your side.