What a cute and cozy site! it already looks very promising and indeed it works well both on desktop and mobile. Good choice on its structure! I'm also always happy to see art on sites, I love your cat sketches omg <3
Also, yay another personal domain user! Love to see more! I personally use both options and I agree Neocities/Nekoweb is a good training grounds if just for small and simple projects, so my mainsite is elsewhere. I needed all the space available xD
Using actual hosts (not saying Neocities isn't, but... you know there's still a difference) helps practicing with more complex and solid tools so there's an advantage in starting with a "full immersion" in web making.
I agree the pictures (like the squared paper used as background for some boxes) load slowly and would probably benefit from optimization. Since it's a squared texture, why don't you try saving it as just one "square" and having it repeat? It'll give you the same result and will load much quicker :) While we're talking about those same boxes, I'd say a liiiitle bit of padding between the text and their edges would instantly improve their readability! ^^
One last suggestion, don't forget to add a links section! No site is an island <3