I found a nice example of English language connotations applied to the original Buddhist ideas. In Chapter 1 of his seminal work Buddhist Precepts and Practice, Professor Gombrich describes his difficulties in translating the sentence ‘What are you religious beliefs’ into Singhalese back in the 1960-s. The closest, even though still somewhat unnaturally sounding rendering turned out to be something like ‘What are your opinions about religion?’ In other words, in the Singhalese culture religious beliefs are or at least not cogntively different from any other opinions you can have about any other matter like politics or science. While this does not tell us anything about the connotations of the Pali term saddhā directly, considering the orthodoxy of the Mahavihara tradition, close relations between the Ancient Indic and all Sri Lankan cultures and etymological relations between the Singhalese adahanavā and Pali saddhā, there is a fairly high chance of the connotations in the contemporary Singhalese and Ancient Prakrit languages being quite similar to each other. Other indirect evidence in support of this would be the possible historical origin of the Singhalese in West Indian Prakrits, with Pali showing a number of Western Indian influences and possibly even originating in the area. This is not all conclusive evidence, but it still provides us with something to work with.
The Western attitude to religious beliefs is very different. ‘I believe because it is absurd’ is an unpopular idea in the Western secular society but it is very deeply entrenched in us. It may be even one of the reasons why people with the scientific worldview are not really fond of religion. However, this cognitive attitude is a thing, and you cannot guarantee it will not mess with your understanding and use of the word saddhā when speaking Pali. That is not say that feeling warm and peaceful when thinking about Dhamma is a bad thing, on the contrary, it is a very good thing. However, we are primarily discussing renderings and connotations of Pali terms, and attaching new connotations to them can be misleading.
Admittedly, I have no knowledge about these things in the Chinese language culture, but I think you can catch my drift 