I know Slate is inert for sure. A compressed and hardened clay.
Lava Rock or Unzan rock as Takashi Amano calls it is also an igneous inert rock.
Depending on where they were collected, the colour varies from dark brown/black to a red colour.
Ohko dragonstone, I have heard, is hardened clay - so this will be ok as well and will not raise water parameters (but I haven't got one to test).
Seiryu as mentioned isn't suitable and will change water parameters. But I'm not convinced all seiryu are equal.
The real seiryu is a Metamorphic Rock from Japan. With their high demand around the world for aquascaping, they are now illegal to export from Japan.
If they are not exporting it anymore, then what are the stones labelled seiryu really? Most of the Seiryu stones being sold outside of Japan are typically Ryouh Stones and are just commonly misidentified.
However, even real Seiryu stones will definitely raise your pH and gH depending on how many per litre you have added into your tank.
Ryouh stone looks very similar to Seiryu.
A lot come from China, some from Japan. But many countries have rocks that can be considered to be ryouh, but obviously they call it a different name. Ryuoh Stones are limestones and they are a metamorphic type of rock, so they will raise your pH over time. Limestones are full of calcium and will leech into the water overtime raising TDS, GH, KH and pH.
Yingshi, I believe this is the same type of rock as Ryouh, but from China.
So same explanation as above.
Manten Stones are an igneous rock that are created from the magma of a volcano. The name was introduced by Takashi Amano.
Just because Takashi san named it doesn't mean that this type of Igneous rock isn't found elsewhere in the world. If you live near a mountain that is considered a dormant volcano, it could be your best bet in getting some free Manten Stones for your aquascape. Unfortunately, they don't occur naturally in Oz. The problem is Manten type rocks do get misclassified all the time. So my advice is to test it anyway if you think you have manten rocks. Soak them in a bucket of water, test the parameters. Then test them again after a week.
A real Manten rock, being volcanic in origin, will not raise your water parameters.
Then there is a similar stone to Manten called Yamaya that is used in aquascaping a lot. For filler or for borders. They are generally small pieces, so they don't get used as a main feature. Aquascapers use this rock to fill gaps in driftwood, or to prop other rocks up, or as borders to larger rocks to draw attention to those feature rocks.
Again this is an Igneous, volcanic rock, that will not change water parameters.
Then there is Petrified Wood which is typically an inert igneous rock. But depending on where it has come from and what rocks it was petrified in, they can raise pH. So again best to test this one just to be sure.
I've come to a personal conclusion that it's too difficult building an Iwagumi style tank for shrimps.
The constant battle with water parameters goes against the stability concept for shrimps.
Simple low demand plants and substrate is so much simpler. But that's just me, I have too many tanks to fuss over and I'm lazy.