Authorities publish changes as they happen: OFAC through Recent Actions and its list service, the EU through the Official Journal, the UN through committee press releases. Aggregators such as the US Consolidated Screening List bundle several sources into one endpoint.
The feed matters analytically because designations are dated. Knowing precisely when a party became restricted is what makes it possible to say whether a transaction was lawful at the time, and it is the backbone of the enforcement chronologies on this site.