Hi,
The extra decimals are necessary in the backend because sometimes you need more than two decimals to configure the price in the backend to get the exact result you want in the frontend when taxes are added.
Even in your example, you need HikaShop to support more than 2 decimals to be able to store 13.7155 in the database so that it can calculate 14.95 when applying the tax. (note that your screenshots do not correspond to the prices you've written about in your message)
It's also necessary for some products where more than 2 decimals are needed.
For example, you'll often see the price of gasoline with 3 decimals, or the kwh price (for electricity).
However, normally, on the frontend you should only see the rounded price with the correct value, isn't it ?
Note that in the past, we had a plugin called "tax override plugin" which could produce strange rounding results. That plugin has been removed from HikaShop but if you still have it and it is enabled, that might explain why you're struggling with the tax calculations and the rounding.