There are typically 4 common classifications for propertie; farm, residential, commercial and industrial.

The property is likely approved for mixed use (commercial and residential).

Your best option is to try to get the landlord to finish the shop and put in insulation for insulation and soundproofing. Outside of that you will probably and in all likelihood need to find a new place which is suitable and move out asap.

Your reason for breaking the lease (if you are in one) would be the landlords inability and/ or unwillingness to address the excessive noise during off hours (usually classified as between 8 am and 10 pm) assuming it is a valid complaint.
You will have to check with your local town regarding the exact noise ordinance.
You will also want to be sure to make your complaint to the landlord in writing and provide them with exact dates and times of the excessive noise experienced during off hours.

Not trying to be an ass but rather providing insight from a neutral position; anything else is on you for not conducting due diligence prior to signing the lease and/ or renewing the lease again despite having these issues.