I think you are looking for a unified solution to deal with very different and very nuanced problems.

The swastika was chosen by Hitler as a means to legitimize his movement. It's important to remember that the average 1920s German had little formal schooling in world history. Even compared to our shitty and revisionist US curriculum, they had next to nothing. He could co-opt it and people were legitimately like, "wow, that's crazy, I absolutely have never heard of Buddhism or Hinduism or anything. Maybe we really did used to rule all of them". The Nazi swastika was at no point a dogwhistle, it's a very explicit and bold statement of their false identity. It was an assertion of power and authority. If you cede the symbol to them, you are intrinsically acknowledging them as the "legitimate" owners of that symbol, which they are not. You can very easily distinguish between a swastika that is being flown as a white supremacist symbol, and one that is not. No Nazis are building Buddhist temples or weaving faux-Native American textiles just so they can have a "plausibly deniable" swastika, nor using pictures of those items to masquerade as non-Nazis with a nudge and a wink (because that would hurt their 'pride'). They just use Nazi imagery directly.

To attack this, you need to very actively de-legitimize its improper usage, and boost its proper usage. The message cannot be "yes, this thousands of years old symbol really is about the Nazis", because that is the stance of the Nazis themselves. It has to be, "fuck off Nazis, that's not your's, and we're going to actively weed out your bullshit".

On the other side are symbols like Pepe, where the purpose was never about legitimizing their ideology, but in fact to hide it and dogwhistle. The creator of Pepe is attempting valiantly to do exactly what I said above, but I think that while getting Nazis to stop using it (and everything else, air included) is great, there is no wider history or adoption that makes Pepe worth using elsewhere. It was just a cartoon frog. In this case, drawing a direct line between people who choose to represent themselves with Pepe, and with the shitty ideologies they're using it to dogwhistle about, is actually the best counter to them, because a dogwhistle isn't a dogwhistle if the relationship is explicit and universally understood.

Banning Pepe outright in Steam profiles makes complete sense to me, because it sends the message that "we know what you're using this to mean, and you're not fooling anyone, dumbass".

Whereas IMO Valve should make it very clear that swastikas will be reviewed, and any Nazi swastikas will result in an immediate ban, whereas use in the legitimate meanings will not be (and that they will take context into consideration, i.e. user location, other profile info, past handles, discussion comments, etc etc).