I think that's a valid interpretation, and if an accurate reflection I think it's important to understand that might be how China perceives it.

"diverting attention away from how countries might want to join together because they see China's growing influence within their borders (both economic and political) as a threat to their sovereignty and independence."

... being another narrative about consequences of China's rise that is a possible lens to view the situation through, and there are certainly people pushing that.

I think the "how it tries to frame the conversation" is missing the other side of the coin: as both US and China "try to frame" the conversation in this way. Pre-2016 we didn't have the same "us vs them" West-China narrative being pushed, but now the narrative of countries relations to China are often framed in this way of "where in the binary division of West/US-v-China does such-and-such a country's actions land".

So I think it's hardly that "China is trying so hard to frame it like this" but rather this is already a dominant strand of the narrative about China in the global media/geopolitical discourse that China is responding to here, not initiating. Which I think is very fair.

If you read more articles on Globaltimes, you'll see them reference the very fears of China being a "threat to their sovereignty and independence", in coverage of various China-related issues that occur in other countries: for example, the crackdown on "foreign influence" in Australia. IMO, China does not try to "whitewash" other country's fears of its rise, and actively reports on those things, tries to relate to how and why a country might have that view, and pushes back against some of the claims.

Also, as an aside, I find the leveling of an accusation of being a threat to "sovereignty and independence" at China, within a discussion of China-US/West relations as quite hilarious, ironical and hypocritical given how many country's seem to pay obeaisance to US' China policy, and even "open up their sovereign lands" to US military bases, etc. Not that I'm judging that, just saying that such an "accusation" definitely can be thrown both ways, and in the US-case the influence is a lot more crystallized and real and with consequences for dissent, than the sort-of "feared" and hypothesized influence threat that China is said to have.

To be clear, I think all countries are vying for influence and will seek to encroach upon the independence and even sovereignty of others to the extent it benefits their interests (Australia with PNG/East Timor/Nauru, for example). So the judgements often come down to assessments about "values compatibility", which is one reason I think it's really important to have your head screwed on straight when trying to view these narratives/views. And one reason it's important to be open to hearing the China side, lest you get the wrong idea otherwise. With all the "othering" of China going on, I bet a lot of people are missing the points where their values, their government's values, and the values of Chinese people, and their central government, actually intersect. Surely not in every place, but I think much more than the "othering narratives" help compel people to see, nowadays.

I think if you're going to talk about the ways that the narrative is being shaped/distorted/framed, then it's important to at least have your head screwed on straight about it. I think you made a good first attempt here, but not entirely accurate.