I see the key issues for Chinese soft power as follows.
1. China is still only a middle-income country on average. Whilst coastal China is approaching Korean living standards, the interior is still way behind. Now, low-income and middle-income countries can rationally admire or respect China, but high-income countries will still look down on China.
But that will change as China becomes high-income and also builds global brands.
I'll repost some of the narratives that China could push globally and which are factually accurate.
2. The West (and in particular the US) is threatened by the prospect of a high-income China which would naturally displace the US. This results in lots of negative reporting on China due to ignorance, outdated information or just plain prejudice.
If we're talking about reporting that tries to be accurate or objective, pointing out factual and analytical errors can work. At a minimum, they'll end up strengthening their China expertise which generally means employing staff who are either based in China or are Chinese.
But there is a lot partisan reporting which doesn't care about accuracy (eg. Fox News). But remember Fox News pushes blatantly fake and extremist viewpoints about the Democrats as domestic enemies. If the US system can't stop even this demonisation from happening, I don't see how China can be expected to prevent anti-China reporting. Plus remember that the Republicans and Democrats both agree that China must be stopped, whatever that actually means.
At the time, South Korean media was really only popular in Southeast Asia and a little bit in Japan with artists like BoA.
In late 2000's, around 2009 or so, with the 2nd generation of Korean wave with SNSD and EXO, South Korea had GDP per capita of 19k, still around 1/2 that of EU countries at 35k+ and US at 40k+. At this point, South Korean media started spreading to China and more broadly in Japan. But it was still seen as a joke in the west given the ridicule given to PSY's Gangnam Style. While SNSD and EXO were big names in China, Japan and SEA, they were relative unknowns in the west.
It was only with the advent of BTS and TWICE in 2015-2017 that Kpop was seen as attractive by the west. By then South Korean GDP per capita was 28k, firmly at 1/2 that of the US and 75%+ that of developed EU countries.
Conclusion: high GDP per capita is the biggest attraction of all. South Korean media did not become attractive until they were at 75%+ the level of a developed country.
More example: in the Cold War era Soviets always had around 1/2 at best 1/3 at worst the GDP per capita of the west. When Russia started dipping below 1/3-1/4 western GDP/capita, people stopped listening to them.
It looks like the minimum GDP per capita for positive media power in the west is around 1/3-1/4 that of the west. Let's say that China gets some discounts for economies of scale and hard power. Let's go with a poorer pre-WW2 traditional developed country: Japan. China got around 1/4 Japanese GDP/capita in 2015-2018. So China only had around 4-7 years so far to effectively develop soft power among developed countries.
Basically, you can't be attractive while a homeless street bum. You can be attractive as a dangerous bad boy (dissident media, counterculture, niche fandoms) when you have at least an apartment and motorbike. But you still need the apartment and motorbike first.