Solid Graphite or bronze impregnated bushing

Where did you get the rebuild kit? Is it a Sherwood kit? I personally don't know the difference but PumpVendor still shows the graphite one.....

I imagine it could break graphite is brittle. We will have to wait for Pete, he’s the engineer 🤓. Personally I would rather the bushing wear than the pump shaft , I just wonder if the bronze is harder than the graphite

Impregnated Bronze is old school. It is used in most Old engines as a pilot bearing for the clutch shaft. It is tough, works and I have not seen any tranny shafts worn due to running in the Bronze pilot bearing. I assume the mention of impregnated means this is an oilite bearing? Oilite bearings were cooked in oil so they would lubricate as they wear.
On the automotive side they tell you to test the bronze with a magnet. If it is magnetic they say it is a cheap copy, if not magnetic you are good.   Also look for a darker color showing it has been heated and impregnated with oil. The shiny bronze or brass look will work but you have to heat it yourself and cook it in the oil which wastes time.
I have done this and you can achieve the desired result but it is messy and takes time.
I used our old Coleman cook stove to do this outside, reducing fire danger. Put some oil in a old coffee can, enough to competely cover the bushing when you drop it in and heat it over the fire till it is very hot, oil nearly catching fire. Drop your bushing in and let it cook, 20 minutes to a half hour and remove and let cool. Once cool it is ready to install. Do not cool it, let it cool naturally.

Graphite may be better in this application but I don't see the bronze option as being bad.
Many electric motors run with this same bronze type bushing as bearings.

Pete you typed faster! I agree with you.