This is the Bohai Sea. It is nowhere near the South China Sea or Taiwan. It is a gulf or arm of the Yellow Sea largely encircled by the Liaoning & Shandong Peninsulas in northeast China, w/ a string of islands in its narrow mouth. The gulf abuts the Tianjin/Beijing metro area.
In Article 2 of its 1958 Territorial Sea Declaration, the PRC claimed Bohai Bay as internal waters enclosed w/in its territorial sea baselines. However, it has not (yet) published coordinates or charts depicting actual baselines in the area.
Instead the PRC's straight baselines along its mainland published in 1996 end at the point of Chengshan Cape on the Shandong Peninsula in the north.
Ordinarily under int'l law, airspace over a country's internal waters is part of its sovereign airspace, where no aircraft have right of overflight. But the US does not recognize Bohai Bay as internal waters & protested this claim w/ a 'freedom of navigation operation' in 2016.
Presumably, the US would recognize a 12-nm territorial sea in Bohai Sea. Due to several islands in the southern half of the gulf's mouth, the entrances to the gulf would still be enclosed in China's territorial sea. (Laotieshan, the widest channel in the mouth, is 22.5 nm wide.)
Airspace above a state's territorial seas also forms part of its sovereign airspace. So whether going by China's or US' legal views, the only way for a foreign aircraft to fly over Bohai Sea, as this U-2 reportedly did, would be to first enter China's territorial airspace.
Ordinarily, aircraft do not have right of overflight above territorial seas either. However, it's likely the US considers the entrance to Bohai Gulf to be a "strait used for international navigation," where the less restrictive regime of "transit passage" applies.
In the UN Convention on the Law of the Sea, transit passage includes right of overflight, with certain restrictions. Restrictions include a ban on "any research or survey activities" without prior consent of the state(s) bordering the strait. States bordering straits can & should
give notice of potential danger to overflight or navigation in straits (such as posed by live-fire military exercises), but can't hamper or suspend transit passage. (Neither "strait used for international navigation" nor "research or survey activities" are defined in UNCLOS.)
Interesting to note that in objecting to the US spy plane's overflight, the PRC Ministry of National Defense did not object to any violation of China's airspace. It instead objected to the violation of a no-fly zone China established during its military exercises there.
The MND said the U-2's trespass of the zone violated the US-China Rules of Behavior for air & maritime safety & "relevant international practices" (xiang guan guoji guanli, 相关国际惯例). http://eng.mod.gov.cn/news/2020-08/26/content_4870115.htm (English) & http://www.mod.gov.cn/topnews/2020-08/25/content_4870094.htm (Chinese)
Probably shouldn't read too much into what this means for China's claims in the Bohai Sea (the Ministry of National Defense is not the authoritative voice on China's legal claims to maritime space; that is instead the Foreign Ministry).
But it is consistent with a trend I've observed in my research: Whereas after the 2001 EP-3 incident and other incidents involving US naval survey vessels in China's EEZ from 2001-2009, China accused the US of violating international law with its activities,
over the most recent decade, China increasingly objects to U.S. military activities along its coasts instead for being provocative and likely to cause accidents, and for being conducted on an excessive scope, scale, & frequency--not for violating international law per se.
This reflects the fact that China's own military vessels & aircraft are now operating more frequently in other states' straits & EEZs, so China wants to preserve general freedom of navigation & overflight, even while maintaining its objections to U.S. activities along its coasts.
As for no-fly zone issue, navies often declare similar zones during live-fire exercises at sea. But specific rules of such zones are not addressed in UNCLOS or other int'l treaties, instead governed by "customary int'l law," i.e. what states do & what they think should be done.
Section V of the US-China MOU on Rules of Behavior for Safety of Air & Maritime Encounters signed in 2014 said each side should establish warning areas during military exercises, & military vessels & aircraft should "refrain from interfering with the activities" in warning areas.
But this was immediately followed by the caveat that military vessels & aircraft "always enjoy the rights of freedom of navigation, overflight..." -- leaving room for disagreement over how to interpret specific scenarios.

https://archive.defense.gov/pubs/141112_MemorandumOfUnderstandingRegardingRules.pdf
Bottom line: It's likely the US spy plane hewed to a bare minimum standard under (debatable) U.S. interpretations of int'l law & agreements. But it's hard to see any compelling reason for the US to fly over Bohai Gulf (of all places) in the middle of a Chinese military exercise.
On the contrary, such an overflight is deliberately provocative. Regardless of whether or not it's technically legal, the United States should avoid such behavior, which has no good strategic purpose and runs contrary to basic principles of crisis prevention and management.
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