Speaking to a lawyer is prudent and I think it's within your best interests to do so.
This is jurisdiction-dependent. While I'm not familiar with Ukraine's platform versus publisher laws, Section 230 is US law and applies to US hosts and American citizens. I would suggest that you review this with lawyers familiar with the law of the country that @yay (the server owner) resides in and the country that you are hosting in.
As far as I understand, CSAM (for American services/hosts) is also similarly covered under Section 230. Twitter/Reddit/Google isn't liable for CSAM found on their platform so long as they act promptly to remove it as soon as it is reported.
Personally, I would be a little more concerned than you are regarding copyright, if only because I've spent a lot of time in the fan-translation space. Websites that host >90% pirated content (e.g. manga aggregator websites) are much more vulnerable to prosecution under copyright law than a website like reddit, who can argue that they aren't a piracy website because a minority of their content is infringing copyright and most of it is OC.
FYI, just so you're aware -- everything that you say in an official capacity as a representative of LemmyNSFW can be used against you as evidence in court.
Consequently, you can't say: "We do not aim to just have stolen copyrighted content on the site"
As that indicates that your website intends to permit (some) copyright infringing content.
You're basically forced to communicate: "We do not permit stolen copyrighted content" (irregardless of how tightly or loosely you privately intend to moderate the content). Alternatively, you should add a disclaimer to your posts that "these views/messages do not represent an official stance of LemmyNSFW and is a personal/individual statement" (something like that).
tldr: Just be very careful of what you say, especially as the content in these discussion threads are easily saved across fediverse instances, and people can always dig up your past statements if something ever goes to court.