That can depend on the material the mulch was, how much of that material was buried, how old that material was, and how healthy your soil is. Wood chips used as a mulch material that end up buried in the soil and then become a soil amendment can occupy the soil bacteria enough so they utilize all the available Nitrogen to digest those wood chips. Once they finish the digestion process that Nitrogen they utilized will return to the soil, as those bacteria die off.
The roots will be digested so slowly that they make little difference in available Nitrogen.

It might be a problem if it was in big chunks that would rot and produce a gas detrimental to a live plant. If mixed into the soil no problem should be noticed. Al

You might want to look up what a nitrogen deficiency in the plants you are worried about will look like and if you see signs of the problem, give your plants some extra feedings. Be careful not to overdo it but something you can use for foliage feeding and perhaps an occasional soil drench might be appropriate for the situation. Eventually the mulch that was buried will break down and help the soil.

I recently bough the house. It's a shredded wood mulch. I'm not sure how old.