It appears you have done a vinegar test for carbonates/ bicarbonates as you mention "bubbling".
Slate from different sources will have different mineral make up. Some flooring slate comes pre-sealed. Your one doesnt read as though it is, so thats good. Give it a good rinse and scrub, then let it soak for 3 or 4 days, changing the water daily. This will leech out most of what might get into your water.
Many people use slate in their tanks without issue. Yours has just been cut into a flooring tile. Only way to know is to try. If you are 100% risk averse, the only safe option is to not use natural products for fear of what contaminents it might contain.