The evidence is the first repair shop saying 'the manifold intake is leaking all over the other parts', suggesting that the other repairs are at risk if that isn't fixed also; and the latest repair person saying 'he squeezed the hose and saw a second lead that requires replacing the whole top plastic part of the manifold'.
That is unusual language to describe a bad manifold or manifold gasket. All the upper manifold is, is essentially an upside down plastic tub that air flows through from the intake snorkel (air filter to tube with airflow meter to throttle body) to the cylinder ports.
Besides the possibility of a coolant passage up through the throttle body, which if leaking would cause low coolant and excessive white "smoke" (steam) out the exhaust pipe, the only other thing it should be leaking is air, into the engine which is a problem because it's unmetered air so it causes a lean running condition.
What could it be leaking all over the other parts? It's a very dubious diagnosis. What other repairs are at risk, exactly how are they at risk? If the intake manifold were to fall apart or leak (worse than it is, IF it's leaking at all), one of two things would happen. Either it would start leaking coolant, either out the side or more likely down into the engine because of vacuum, producing white tailpipe smoke or possibly hydrolocking the engine (which IS a big deal, can ruin an engine if it suddenly puts a lot of coolant down in and the engine is at load, otherwise a slow leak with it at idle will typically only stall the engine), and you'd start getting misfires and notice your coolant disappearing.
- OR - if it starts leaking air you might have a poor idle, loss of power, engine misfires, and the only thing that happens if it's not fixed is the car doesn't run well if at all until it's fixed.
As far as
"squeezed the hose and saw a second lead (leak?) that requires replacing the whole top plastic part of the manifold" this is also a strange statement. I've asked more than once what make/model/engine you have but in general there is only one (pair of) hoses on the intake manifold but on the LOWER not upper plastic, going to and from the heater core. Yours may not be set up like this, heater core does not have to attach there but does not attach to a plastic upper intake manifold (I suppose very bad engineering could do that, but there is no reason to).
Could he have meant he squeezed the upper radiator hose and coolant came out of the thermostat housing, not the upper intake manifold, or is this some strange design where the upper intake manifold and thermostat housing are molded into the same piece (which also would be a strange/bad design)?
Either the person making the diagnosis has very bad communication skills and doesn't know what engine parts are called (okay to be fair I made up the term snorkel above, it's not an official term ) or it's a made up diagnosis of the type shops use to milk people out of money for unnecessary repairs. These types of diagnosis-scams often don't make sense.
Is the vehicle not running properly
now and if not, what are the symptoms? If it is not running lean/rough and you aren't losing coolant, it is very unlikely that you have an intake manifold leak. If the side of the plastic manifold, near the EGR looked charred and brittle/crumbly from heat, that would be a reason to expect a failure soon, but not a leak w/o other symptoms and that's not at all what you're stating.