Mechanical isolation to reduce direct sound transfer.
You have your pump fixed securely to the wall so it can essentially ‘grab’ the wall and shake it at 50/60Hz even if you have rubber mounts. I have similar problems with air pumps.
So I get very strong bungee cords and make a four-way harness to suspend the pump in the air, not connected to the wall. I see your pump is attached to flexible hose with jubilee clips so that solution is totally possible with your setup.
“Do it Yourself Isolators
In less sophisticated solutions, bungee cords can be used as a cheap isolation system which may be effective enough for some applications. The item to be isolated is suspended from the bungee cords. This is difficult to implement without danger of the isolated item falling.”
Basically, make sure the cords can’t just slip off with the vibration by liberal application of zip-ties etc.
To deal with the vibrations through the hose, you need an expansion chamber.
Fit one as close as you can get to the pump and it will even out the pressure waves that are causing vibration down the hose past the expansion chamber.
As you can see, pumps that come with one fit it directly to the pump.
In my experience there comes a point where making a low quality pump perform like a high quality pump costs more, and is less reliable, and less effective, than just buying the expensive but good pump. The cost is spread out over longer but often the cost is more, for an inferior performing part in your system.