Does the Russian region of Kaliningrad "now belong to Belarus," with NATO forces supporting Minsk in its struggle against Russia? No, that's not true: No parties allegedly involved in the supposed confrontation issued any statements confirming the purported annexation, and no credible sources corroborate the claim.
The claim appeared in a video (archived here) published on YouTube on August 25, 2023, under the title:
Kaliningrad Now Belongs To Belarus with NATO approval! Lukasenko-Putin on the Brink of War!
At the 0:20 mark, a male-sounding narrator said:
The secret documents revealed by Lukashenko have proved that Kaliningrad does not belong to Russia. The NATO army has taken action to take the city of Kaliningrad from the hands of Russia. Kaliningrad is under blockade by US Navy ships. Kaliningrad is no longer a Russian territory.
Here is what it looked like at the time of writing:
(Source: YouTube screenshot taken on Tue Aug 29 16:49:11 2023 UTC)
Kaliningrad, known as Koningsberg before 1946, is a region of Russia located nearly 800 miles away from Moscow, and separated from the rest of Russia by other countries.
(Source: Google Maps screenshot taken on Tue Aug 29 19:17:54 2023 UTC)
The city of the same name as well as the surrounding area was transferred from Germany to the Soviet Union after World War II, but that was only finalized in 1990. When the USSR ceased to exist, contemporary Russia inherited the region.
No sources confirm that Belarus, a close ally of Russia, made any territorial claims on Kaliningrad in August 2023.
A search for the sentence "Belarus annexed Kaliningrad" on Google News does not produce any relevant results.
A Google search across the NATO website shows that this organization did not publish any updates involving Kaliningrad between August 1 and August 29, 2023:
(Source: Google screenshot taken on Tue Aug 29 20:30:15 2023 UTC)
The official website of Belarus does not mention Kaliningrad as its region.
According to the website of the president of Belarus, Alexander Lukashenko met the Russian governor of the Kaliningrad region on June 5, 2023. But that event took place in Minsk, and the official press release cited Lukashenko aiming to foster cooperation, not declaring war:
I am sure you will agree with me that the unprecedented attempt made by the West in 2022 to limit our communication with you, the free movement of goods by rail and road transport both from Russia and Belarus - this attempt was doomed to failure. No matter how hard they try to divide us with artificial barriers, it will not work.
Lukashenko referred to the events of the summer of 2022, when Lithuania attempted to ban the transit of the items sanctioned by the European Union from Russia to Kaliningrad through its territory. The issue, however, was resolved within weeks.
Had Belarus annexed Kaliningrad in August 2023, the U.S. Department of State would likely issue a statement on such a major geopolitical issue. However, a Google search for the words "Belarus" and "Kaliningrad" across its website only shows pages with the current status of all U.S. sanctions against different countries, and nothing in this document indicates that any new restrictions were introduced in connection to the purported annexation of the Russian enclave.
Even the website of the Russian president does not say anything about Kaliningrad in August 2023: As the screenshot below shows, the last time the name of this region was mentioned there was March 30, 2023.
(Source: En.kremlin.ru screenshot taken on Tue Aug 29 19:04:23 2023 UTC)
What credible news organizations report about the issues involving Belarus in August 2023 is that the tensions have been growing for months at the border between this country and Poland, a NATO member. But, as of this writing, that hasn't led to any active combat.
Since the 2022 Russia's full-scale invasion of Ukraine preceded by the annexation of Crimea and occupation of other territories in Eastern Ukraine, claims about Kaliningrad resurfaced on social media more than once. Lead Stories debunked some of them here.