If all liquid stuff inside the Earth turned solid, what would be the effect?

This process is actually ongoing. The Earth is cooling, and the liquid outer core is gradually contributing to the growth of the solid inner core, which increases in radius by roughly 1 mm each year.

You’re right that solid iron is denser than liquid iron, so a fully solidified core would shrink. However, the process would take hundreds of millions of years and the Earth’s diameter would decrease perhaps few tens of kilometers but that likely wouldn't be enough to cause major structural collapse.

The effect on plate tectonics, however, would be decisive. The latent heat released as the outer core slowly solidifies drives convection in the remaining liquid core, which in turn generates the Earth’s magnetic field. It also helps sustain mantle convection, which keeps the tectonic plates moving. Without that heat flow, plate tectonics would eventually cease, and the planet would instead develop widespread contractional features such as thrust faults. This will happen eventually, so the question is not purely hypothetical.

We can look to Mars to see what happens when a planet's inner and outer cores solidify. Once the solid iron core can no longer spin within its liquid metallic shell the geomagnetic dynamo loses power, and a planet's magnetic fields fade, then disappear leaving its vulnerable atmosphere to be bombarded by the suns ionic wind. In the case of Mars, this solar wind has stripped it of a large part of its atmosphere and by extension, its water. As far as I know, there aren't any globally prevalent tectonic features on Mars that indicate "shrinkage" on a planetary scale due to cooling of its core.