You have an air leak on the priming system.
So either the bulb is leaking or the gasket behind the air box is leaking
Very common with the air prime system.
The plate warps particularly if the owner overtightens it.
A lot of times the air purge B & S engine need 2 gaskets to make up for the warping.
As for repairing cheap imported mowers that have no service logistics, I for one don't do it.
While we all enjoy a challenge, in the long run it is against the interest of mower repair shops to service disposable mowers.
If we keep them running they will dominate the market & we will all be out of a job.
When a shop brand comes in to me I always over quote substantially to cover the cost of faffing around trying to find parts that will fit.
Just sent a pressure washer back with a $ 400 bill for fixing an oil leak which ended up being because the hole in the crankcase was machined too big allowing the seal to spin in the case when the case got hot enough.
The engine was a GX200 knock off and just for interest I checked the fan against a real GX 200 one after I had worked out what was happening.
The copy was 20mm smaller in diameter had 5 less fins and was 10 mm shorter in height
the breather tube had crumbled away filling the sump with rubber fragments and the HT lead was cracked everywhere so when it got damp it shorted
The fuel tap on the carb broke off and a genuine Honda one had to be cut thinner to fit.
The fuel cap had fallen apart so the owner had siliconed it back together blocking off the vent.
The retaining bolt for the air filter cover had also broken away and the foam air filter did not make a seal against the air box.
The customer was told ( and they believed them ) the engine was made at the same factory that makes Honda engines and Honda parts would fit ( they don't )
The washer is 18 months old and had been used twice, but it was $ 700 cheaper than the real Honda one.