There is no official, published list of in-scope companies, either by the UK Home Office or any other entity. This is because the list itself cannot be exhaustive, unlike Australia where such a list is published as open data. Consequently, "Required" means that for the last financial year of that supplier, the data your supplier has submitted to Companies House or other Government filings platforms indicate that the company is very likely to be in scope for compliance with that particular regulation. It is possible that they are not in scope, but this is not something that can be determined using data they have made available publicly.
This is one of the key challenges Governments have with enforcing legislation and something that is very easily resolved on an interactive, collaborative platform like TISCreport. You are able to narrow down your suppliers to a smaller list of potentially non-compliant companies, and use the system communications system to fill in the missing gaps.
If your supplier appears to be in scope but has not complied with that particular regulation, your next step is to invite them to either comply or submit an exemption statement explaining why they are not in scope. This will enable all other buyers to be able to benefit from your due diligence efforts with that supplier and vice versa.