On the test build the tech description says, "reduces production cost of starships and stations to 70% of their base cost."

The Shipyard planet build item says, "build large starships by +2 hull tiers." Says nothing about reducing production cost.

What do shipyards do exactly now?

It does both. The Shipyard hull itself provides the discount. Each of the construction yard modules allows +1 hull tier.

You can change the design of the shipyard to remove the construction modules, it'd still give you the 30% discount on building ships (and orbital stations); but you would need to build something else to get the construction modules to build large ships.

For example, with improved solar panels, you can get rid of the nuclear reactor if you remove one construction module from the shipyard. You can then put two science labs to replace the removed module and reactor. Then the description in the planet screen will tell you "+1 hull tier" and "+4 research".

Is that bonus supposed to stack? For example, if I have 2 Shipyards at a Planet, should I be getting it down 49% cost?

No, it doesn't stack. A ship can only be in one shipyard at a time.

Ok, thanks for the explanation.