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So I have found a solution, for anyone interested in how :
By checking this chart.js doc, you can find an option called offset which will create as explained an extra space.
Then to get the exact result I wanted, you hide the X axis.
Which gives us this :
x: {
grid: {
drawBorder: false, // hide the x axis
},
},
y: {
offset: true, // create a sensation of space with the x axis hidden
},
Source:stackexchange.com