Hi my friend,
Let me just start this post by saying that sadly I don't think I can be much help. But I want to give back to this awesome Melonland community and am trying to find posts with no replies that I can contribute to. Now let me elaborate on that by saying, I have done web development for many years, and I think the reason why you're not getting any responses on this post is because you're asking about something that is fiendishly hard and kind of scary to implement. As soon as you're taking money for products you are kind of opening a Pandora's Box of legal and security concerns. Even if you're using a plugin or frame for payment, vulnerabilities on your page can still expose credit card info to hackers. That's why it's very uncommon to see anyone but big companies having a storefront directly on their site - and honestly nowadays even a lot of big companies don't bother. Even if you do see a storefront directly on someone's site, it's often just a third-party storefront that they paid to rebrand and route to from a subdomain of their site or something like that.
Looking at the scale of your Kofi, and assuming people actually are buying these things regularly and subscribing, I hate to say it but I don't think you really can move that into your own site. It would be a job for a paid developer at the very least, and even then I'm not sure it would be worth it since most people are vastly more comfortable making payments on established familiar platforms. Especially stuff like subscriptions.
I will say maybe there's some more customizable payment platform out there to do what you want, but I researched this myself for my internet radio site awhile ago and didn't find one. In the end I ended up just using a Square payment link to take donations.
I think that if you REALLY wanted to move more of it to your site, my honest recommendation would maybe be to just have a page that lists what you have for sale, along with prices, and that links to your payment platform for the actual heavy lifting. In other words, just keeping the Kofi and adding your own sort of "mirror image" page of it in your own style on your site.
Sorry to be a naysayer, but this is just one of those things that is not too feasible for an indie website to do

perhaps a developer with more experience in the payment space can correct me, I would love to learn otherwise.