The easiest way to see if a connection already exists is to use the search field at the top of the connections homepage (the grey box labelled Connections). When you click on it a free search box appears independent of the categories which indeed are a bit arbitrary.

The one at Stara Nekrasivka (Ukraine), though, looks like an obelisk to me :) Or maybe it's not tall enough to qualify as such?

I'd like to propse another one under "Individual People Connections": Xuanzang

Xuanzang, born Chen Hui / Chen Yi, was a Chinese Buddhist monk, scholar, traveler, and translator who traveled to India in the seventh century and described the interaction between Chinese Buddhism and Indian Buddhism during the early Tang dynasty.

- Ajanta Caves - Xuanzang visited Ajanta.
- Bamiyan Valley - In Bamyan, Xuanzang met the king and saw tens of non-Mahayana monasteries, in addition to the two large Buddhas of Bamiyan carved out of the rockface.
- Buddhist Vihara at Paharpur - After Nalanda, Xuanzang traveled through several kingdoms, including Pundranagara, to the capital of Pundravardhana, identified with modern Mahasthangarh, in present-day Bangladesh. He also visited Somapura Mahavihara at Paharpur in the district of Naogaon, in modern-day Bangladesh. The modern-day vihara however dates from the 8th century AD, after Xuanzang.
- Grand Canal - The Grand Canal passes through Luoyang, where Xuanzang was ordained as a śrāmaṇera (novice monk) at the age of thirteen.
- Lumbini - In 636, Xuanzang traveled through Terai in the southern part of modern Nepal, where he found deserted Buddhist monasteries, and thence to Kapilavastu, his last stop before Lumbini, the birthplace of Buddha. In 637, he set out from Lumbini to Kusinagara, the site of Buddha's death.
- Mahabodhi Temple Complex - Xuanzang visited Bodh Gaya in 637.
- Nalanda - After Bodh Gaya, Xuanzang went to Nalanda, the greatest Indian university of the Indian state of Bihar, where he spent at least the next two years.
- Samarkand - Xuanzang crossed the desert from Tashkent further west to Samarkand. In Samarkand, the party came across some abandoned Buddhist temples and Xuanzang impressed the local king with his preaching.
- Silk Roads - The Silk Road passes through Luoyang, where Xuanzang was ordained as a śrāmaṇera (novice monk) at the age of thirteen. / After his return to China in AD 645, Emperor Gaozong of Tang ordered to install two stele stones in celebration of Xuanzang's extraordinary achievement at the Giant Wild Goose Pagoda. There is also a statue of Xuanzang at that pagoda.
- Taxila - Xuanzang visited Taxila, which was desolate and half-ruined, and found most of its sangharamas still ruined and desolate.
- Xinjiang Tianshan - In 629, Xuanzang traveled across the Gobi Desert to Kumul (modern Hami City) and then followed the Tian Shan westward to arrive in Turpan in 630. The hottest mountain in China, the Flaming Mountains, is located in Turpan and was depicted in the "Journey to the West", a Chinese novel that is an extended account of the legendary pilgrimage of Xuanzang.

Source: Wikipedia

He has one already, Jurre: https://www.worldheritagesite.org/connection/Travels+of+Xuanzang

Let me check if you found new connected sites - I'll add them.
P.S. at least you extended it and added notes for all of them, so the work was not in vain!

Thanks for noticing! Should have used the search option, I guess...

There's even another one, as we broaden the connection a bit beyond his travels: Part of Xuanzang's remains were taken from Nanjing by soldiers of the Imperial Japanese Army in 1942, and are now enshrined at Yakushi-ji in Nara, Japan (wiki)

Could "Captain James Cook" under "Individual People Connections" be renamed "James Cook"? It seems weird to have his title "captain" in front of it while this is not the case with others. Just a question of being consistent.

As a counterpoint, I'd mention that in much of the English-speaking world where he traveled, he is better known as Captain Cook than as James Cook. You can see evidence of this with the number of tourist attractions with Captain Cook in their name, rather than James Cook. I'd recommend keeping the Captain in the full name of Captain James Cook for the connection.

And another one for "Individual People Connections": Giosafat Barbaro, a Venetian diplomat, merchant, explorer and travel writer

- Aleppo - After the death of Uzun Hasan in 1478, Hassan's sons fought each other for the throne. Barbaro hired an Armenian guide and escaped by way of Erzerum, Aleppo, and Beirut. He reached Venice in 1479.
- Corfu - In 1473 Barbaro traveled to Cyprus by way of Corfu, Modon, Corone and Rhodes.
- Pasargadae - Giosafat Barbaro was the first European to visit the ruins of Pasargadae, where he believed the local tradition that misidentified the tomb of Cyrus the Great as belonging to King Solomon's mother.
- Persepolis - Barbaro visited the ruins of Persepolis, which he incorrectly thought were of Jewish origin.
- Rhodes - In 1473 Barbaro traveled to Cyprus by way of Corfu, Modon, Corone and Rhodes.
- Venice and its Lagoon - Barbaro was born in Venice and was a member of the Venetian Barbaro family. He became a member of the Venetian Senate in 1431.
- Yazd - While in Persia, Barbaro visited Yazd.

Source: Giosafat Barbaro

For Silk Roads:
Already inscribed, still on T List: Chinese Section of the Silk Road: Land routes in Henan Province, Shaanxi Province, Gansu Province, Qinghai Province, Ningxia Hui Autonomous Region, and Xinjiang Uygur Autonomous Region; Sea Routes in Ningbo City, Zhejiang Province and Quanzhou City, Fujian Province - from Western-Han Dynasty to Qing Dynasty

Any guess if the 2 other (identical) T-list items are either an extension or new WHS?