I have two websites that have different purposes, but in retrospect I wish I just had one main website. The main reason is that when I made my
first website, its intention was to just host my webcomic and nothing else, but over time it just turned into my 'personal' website for everything I do, especially since I stopped using mainstream social media and never got into the concept of participating in servers/etc. either.
I wouldn't say my concern is that it's 'difficult' to upkeep both websites (though YMMV) so much as
the other one's purpose is so specific (all it basically does is host a webring) that it seems a little 'pointless' for me to have it, other than the fact that I already bought the domain, and, well, I do really like its domain.

Of course, since I pay for my own websites and domains instead of taking the free Neocities/Nekoweb/etc. route, I do feel like there's a little more investment to consider. If you're making a second website on a free host it's not as big a deal. Even if one website ends up being less 'updated' than the other, it's not like there's a
requirement to update a website regularly, so the issue is more about your personal expectations for yourself.
Personally though, if my desire was just to have a different visual style/theme for the website, and the second website doesn't have any actual content that significantly differs from the first one, I might prefer to just have different themes for individual webpages or a menu that toggles between themes. Sure, you might have to spend a bit more time styling the second theme and fiddling around with how to actually set it, especially if you have to toggle whether certain images get displayed or not too and not just changing the colours around, but you'd have to do only marginally more work than you would if you made a second website.
I think the main consideration is thinking about how you'd split the content between websites. Sometimes I find myself at a loss whether something I want to do is suited for my one website or the other, since even though they have different purposes, they overlap well enough that it doesn't really matter. If your websites had a clearer distinction between their purposes it might not be as troublesome for you to decide.
Of course, if you wanted a second website just to give it a different name than your current one like how I did that's as good enough a reason as any.