pH should be stable, but the level of hardness, or GH, is more important than pH. We should aim to keep our fish in water with similar hardness as the river or lake where the species originated. This means either choosing fish that come from similar hardness to our tap water, or changing the tap water to suit the hardness needed by a species we want to keep.
The pH can be slightly outside that of the water the fish originated in, as long as hardness is within their range.
Websites such as Seriously Fish give the hardness range that a species should be kept in, with the middle of that range being better that the bottom or top end.
Using peat doesn't affect hardness, though it can lower the pH provided KH is not too high. The only way to reduce hardness is by mixing tap water with pure water such as reverse osmosis or distilled water.
Hardness is the measure of mainly calcium, some magnesium and trace amounts of other metals. Peat will not remove these from the water.
KH is the measure of the amount of buffer in the water, mainly carbonates. KH buffers the water and stops pH changing. When the KH is low, it is easy to alter pH and here peat can be used to lower pH. Where KH is high, it is much harder to change pH, so peat will have little effect.
Words like slightly hard can be misleading. We have had members who said their water company used the term hard when in fish keeping terms, it was borderline at the top end of soft. If you could find a number for your hardness (look on your water provider's website) we would have a better idea.