"I.e. the Ukrainian pronunciation of the Cyrillic letter г?"

Yes, that.

"Is there any language where voiceless [h] and voiced [ɦ] form a phonological contrast?"

I cannot answer such a complicated question.

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Anyway, this Chinese character meaning exorcism...

https://qph.cf2.quoracdn.net/main-qimg-0b91eeb27763772311f3eca347868fd5

...may be even more complicated than biáng that we discussed a few years ago. The pronunciation is not given.

And what about this monster? It may not be a real character.

The only reference to it I was able to find was on the Uncyclopedia website, which is a website where you can: “Discover, share and add your best comedic writing!” So dhō is thus very probably just a recently invented character invented for fun...

https://2.bp.blogspot.com/-SGLGSY3WOTU/XBNysgYEXGI/AAAAAAAABuA/X7xj9LbAITEOPFk1nMoXeFDwMLx9-oDcgCLcBGAs/s1600/1Dho.tif