"제가 허리띠를 차고 있습니다."
Translation:I am wearing a belt.
I fully understand that ~고 있다 makes present progressive as you pointed out. However, I suppose that present progressive is not obligatory to translate ~고 있다 for state verbs. Because present progressive of state verbs looks strange (e.g. I am knowing him, you are liking dogs, she is being young).
In many languages, including my native languages, "wear" is an action verb (aka dynamic verb). So you shouldn't apply English grammar rules so rigidly to other languages.
When a person is in the process of putting on their belt and someone knocks on their door and asks what they are doing, in such context, saying "나는 허리띠를 차고 있어" would be an appropriate response. This can be translated into English as "I'm wearing a belt" and it doesn't sound strange at all. Naver's Papago also translates it to "I'm wearing a belt."
I have never applied English grammar rigidly to other languages. Korean has its own grammar and I know "차고 있습니다" is completely correct in Korean.
The reference  says "wear" is stative, and the reference  says "in English the same verb wear (stative) or put on (dynamic) is used uniformly".
The point of the discussion is that "wear" should be accepted as well. Note, I have no intention to eliminate "is wearing" from correct answers. "나는 허리띠를 차고 있어" can occasionally be translated as "I'm wearing a belt", but not limited to.
Naver's Papago is nothing more than an machine translation. A machine translation is useful, but not always perfect.
 Suk-Jin Chang (Seoul Nat. Univ.), "Korean", John Benjamins Publishing Company, p. 235 (1996)
I only replied to the part of your earlier comment where you said "present progressive of state verbs looks strange".
I didn't say you're wrong for using just 'wear'. You can anyway report it. If it is indeed acceptable, the contributors will add it. What people say in the comments doesn't matter.