Interesting. I have spatial sequence synesthesia [0] and number form synesthesia [1] and this feels a little weird to look at. It disagrees with my mental model of dates. But that's just me.
It's very hard to describe as it's a structure that exists in my "mind's eye" and difficult to understand it. In fact, what I am about to write will probably sounds a bit bonkers.
I am able to switch to different views depending on the scale. For instance, when thinking about the week I see one thing than when I think about a period spanning years.
The week-view is very much linear at the start of the week but something weird happens near the weekend - it kind of twists back to the start - I can see the following week when I am thinking about Saturday or Sunday.
The yearly-view does a similar thing around winter and spring. The depiction on your site is actually somewhat representative of the general shape - if you take it and twist it a bit in 3D space you kind of get to what I see.
I realise all of this sounds insane haha. I honestly didn't even know it was a thing until a few years ago when I happened to read about it.
Anyway, cool project, I hope it takes off. My only feedback would be that the minimalist website design makes it a little hard to parse information (especially the pricing screen).