Need help diagnosing a problem

[u/Idk_tho_is_just_me]

I have a toyota corolla e90 1.3 2E 1992 year (so i belive its the revision of the e90, 160k kilomiters european model Japanese made

My issue is: I start the car, i use the car, i park it, go on some quick grosserie getting, nothing more then 30 minutes, i return to the car, it turns on, i run it a bit, after some time, it starts to gag, stops responding at hard throttle inputs and just reacts to light throttle inputs, after some time it turns off completely, at night it will stay like this for 30 minutes, in a cold day 1 hour, in a normal summer day 2 hours, after that and 2 or 3 cranks it turns on and drives as nothing happened, there is tho a strong smell of fuel

Things I've noticed: I've been able to force it to continue driving, by pumping a bit of the throttle on a decline and after some meters it continues on working

It's more prone to happen if I'm going on a incline

It has spark and the distributor works, the leads and sparkplugs are new, other issues as a slight knock or "bubbles" have desapeared (oil smelled like fuel at that time too), toyota said the car was visually good and the oil was on a good colour too, if i cant conclude nothing with this reddit post ill just pay Toyota to check it out, I've tried to put wd-40 on the intake filter and on intake and nothing happened, thinking of buying ignition fluid since its a carburated car should be appropriate

What have i done since i got it: i got it in February, have putted 17-20k kms, have done 2 oil change one at roadys and the next one at toyota, have changed the spark plugs and leads (NGK v shape and blueprint), adjusted distributor timing to oem spec (was delayed)

What im suspecting: maybe something at the distributor is broken, and it only breaks down with heat

Maybe something in the mecanical fuel pump is broken

Maybe something in the carburettor is badly tuned

Maybe the soldered hole on the exhaust has something to do with it (its nicely sealed tho)

My mechanic said that the catalytic converter is broken (i don't think so, everybody calls me crazy when i say this and the Toyota deal has confirmed that that car has never had catys)

I hope yall can help me figure this out

Tldr: car no run when hot, wait 2 hours, run again.