I've always thought of artisan more in terms of style, not individual. When I see something like "artisan glass", I know it's been hand crafted by an individual artist, that it is unique and likely to be one of a kind, and that the creator is an artist who works in glass, as opposed to someone who simply makes glass items.
The distinction of artisan, to me, is more about the form or style of the product. When it applies to soap, if I were looking at three different soaps, I might see three different types - not based on criteria like vegan/nonvegan or botanical colored/mica colored, etc - but more based on their form.
Soap A might be produced by an individual soap maker, who focuses on formula vs artistic appeal. You can go into their shop or online store and buy more of the exact same soap any time, and it will always looks the same or similar. This could be an expert soap maker who produces high quality soaps that are lovely to use, but I would not look at their soap and think of it as artisan soap because I could walk into their shop a year later and buy a nearly identical replacement of my bar.
Soap B might be more creative in its form, involving more elaborate styling like piped tops, embeds, etc, or take more unusual forms, like cake slices, cupcakes, watermelon slices, etc. but again, you can go in at any time and buy more cake slice soap etc, because that is what they focus on producing. Again, it could be produced by an expert and it could be truly lovely soap, but I would not look at it and think "artisan".
Soap C might be unique in any number of ways, from shape or style to formula or ingredients, but if I buy this soap I see here right now, I won't be able to buy it again because that soap maker focuses on the artistic angle of soaping and never reproduces a design. They may repeat a style, such as ebru painted soap, but you'll never see the same design, because as an artistic approach, they are always wanting to create something different. So, if I walk into their shop a week later, I probably won't be able to buy another bar of that exact design, because once that batch was done, they moved on to a new artistic idea. I'll never be able to buy the same soap twice because of this. They might be an expert and make lovely to use soap, or they might *not* be made by an expert in soap recipe formulation, might only have a single recipe they use for every batch, but because their designs are always new, I'm going to think of their soap as "artisan".
I realize my perspective on this is very strongly influenced by my art background, but for myself, that's what distinguishes between creatively crafted and artisan.
Just my 2¢