In this case, it seems last week's sanctions have been coordinated with other G7 countries, from the US State Department's press release in May '23 (selective quote):
Today, the United States, in coordination with the G7 and other international partners, is strengthening the unprecedented global sanctions and other restrictive economic measures to further degrade the Russian Federation’s capacity to wage war against Ukraine. The U.S. Department of the Treasury’s Office of Foreign Assets Control (OFAC) is implementing new commitments made at the G7 Leaders’ Summit to hold Russia accountable for its war.
This reporting requirement is designed to provide additional information and fidelity on the Russian sovereign assets immobilized in U.S. jurisdiction. It is consistent with a similar measure recently adopted by the European Union and implements the G7 Leaders’ commitment today to take steps to fully map holdings of Russia’s sovereign assets that will remain immobilized in G7 jurisdictions until Russia pays for the damage it has caused to Ukraine.
For example, Al Jazeera reported on Japan's announcement to step up the sanctions (a week after the US press release):
Japan has announced additional sanctions on Russia after the Group of Seven (G7) summit the country hosted last week agreed to step up measures to punish Moscow over its full-scale invasion of Ukraine.
In coordination with other G7 members, Japan will freeze the assets of 78 groups and 17 individuals, including army officers in Russia and ban exports to 80 Russian entities such as military-affiliated research labs, according to a foreign ministry statement released on Friday.
Some explanation of how the sanctioning and enforcement works in practice
Restricting their access to do business with US companies (and international partners who agreed with the same / similar sanction regime).
The idea is as follows. The US sanctions Russia, they want to discourage companies to do business with certain Russian entities. For US companies it's simple, they could be charged in the US for violating some US law.
Now let's say they want to discourage some Turkish company from doing business with some US sanctioned entity. That Turkish company probably also deals with entities in other countries, probably including the US (based on the US dollar being the world reserve currency and a lot of international transactions being settled there). They could forbid US companies from doing business with that Turkish company once they find they still do business with a sanctioned entity.
An example of this was reported in Dutch news when a Dutch businessman appeared on the US sanction listed, supposedly for filling orders for Russian intelligence. According to NLTimes (large quote, but it really paints the picture of how it's applied in practice):
For the first time since Russia's invasion of Ukraine, a Dutch citizen has wound up on a list of sanctions from the United States. Edwin Onno van Ingen, 58, was added to a list established in 2021 by the U.S. which freezes the assets of anyone accused of providing support to the Russian military or the country's economy. It also punishes those participating in various acts of corruption on Russia's behalf, like interference in the elections of a U.S. ally, cybercrime, transnational corruption, undermining political stability, or participated in an assassination of an American or American ally.
The U.S. Department of the Treasury said in a press release that Van Ingen "is a primary Europe-based procurement agent for Russian laboratories focused on nuclear weapon design and development as well as research on advanced conventional weapons technologies. Russia’s intelligence services often task Van Ingen to solicit offers and procure technologies such as advanced manufacturing, scientific, and measuring equipment. Van Ingen then approaches manufacturers and resellers and, in many cases, helps mask the real end-user of the equipment being bought and helps organize the equipment’s transshipment to Russia."
The update was discovered by Dutch publication Follow the Money. Van Ingen told the publication he was very surprised when they informed him of the sanction. "What you say is completely new to me." A review of records maintained by Open Sanctions showed that Van Ingen is the first Dutch citizen to be added to one of the U.S. sanctions lists. He told Follow the Money that his father did business in Russia for decades. After he died, the younger Van Ingen picked up where he left off, but stopped making deliveries to Russia after the war began.
Van Ingen also does not try to evade restrictions by sending shipments to intermediary countries, like China or Turkey, he stated. He runs several Dutch businesses, including a business material wholesaler, and providing company administration to small businesses. Follow the Money said he also owns mediation firm Ronin Management BV, for which he was sanctioned. The company has an estimated balance sheet reflecting about 10 million euros.
“I have never done anything that the Ministry of Economic Affairs does not know about,” he told the publication. "I was not approached by anyone from the U.S., nor by The Hague," he added. "I'm getting negative attention now, this is what the U.S. is making of it, but I haven't done anything wrong." His other companies have also been sanctioned, specifically Pro Rata Solutions B.V. and Delta Technical and Scientific Instruments B.V. Like Van Ingen, these were sanctioned under Executive Order 14024. The names were among those added to a list maintained by the Office of Foreign Assets Control strictly because of Van Ingen's involvement. Neither he nor his companies can do business with an American entity, the Treasury Department said.
Aside from just banning access, foreign companies can often be prosecuted (e.g. because money passes through a US company). For example, this article on visualcompliance.com cites such cases with Australia and Hong Kong based companies:
Between 2013 and 2019, an Australian freight company handling cross-border shipments accidentally worked with entities on the OFAC Specially Designated Nationals (SDN) and Blocked Persons list, including Iran and Syria, triggering OFAC Compliance infringements.
Because the transactions involved the U.S. financial system, OFAC issued 2,958 violations, highlighting that even companies outside the United States must follow sanctions screening best practices if their commercial activities involve U.S. entities.