Firstly it would be a real big help if you posted the engine number ( Model & code ) .
I will assume that it has the 4000 seriec Briggs & Stratton which has an impulse pump.
That being the case did you fit it correctly?
The impulse line goes to the inlet in the middle on top
The fuel input & output are the ones ones the side.
Sounds like you have installed it incorrectly.
Now we need to get the facts strait and in chronological order.
It was serviced and had a carb overhaul after which the engine ran fine with the exception of the fuel leak.
The engine was pumping fuel into the crankcase but apart from that was running fine.
You replaced the fuel pump and now it won't throttle up.
Is that the correct time line. ?
Check the impulse line as requested and check the fuel pump as requested let me know what you find.
If the fuel pump you fitted was an unbranded one from China via an internet only seller then good chance it is trash.
Down here I have found several customers who fitted a $ 10 fuel pump bought off the net that had a neoprene diaphragm fitted so it went to jelly after a few months and in one case wrecked the carb and nearly the engine to boot from running lean which is why this one came into the shop as it was that hot it started to smell funny.
As for the other bit.
A lot of shonks make a lot of money by exploiting the greed / selfishness of the population by importing garbage from China for next to nothing then selling it on evilbay / Craigs / amazon etc for about 10 times what they paid for it .
Most of it comes from factories who "make a million for me that look exactly the same as this" and are unfit for the purpose if they fit at all.
Note not everything that comes from China is garbage , some of it is good and some of it is actually OEM parts, but sorting out the good from the garbage is not easy.