Vectorizar logo

I'd say you did this correctly by creating it in Illustrator and exporting an .svg from there.

I really don't see why you should introduce a raster editor like Photoshop into the mix. That can only cause problems, because the chances are very high that your vector content will be rasterized.

Anything created as paths will be rasterized in Photoshop! No exception. Only shape layers and in some cases text will survive as vector data.

In addition, as c.p. points out, Photoshop will always render vector data as pixels on screen, at the base resolution of the document. In a true vector application like Illustrator, vector data are always rendered at full screen resolution regardless of reproduction scale.

In short, leave Photoshop out of it! Keep this in Illustrator.

If the logo can be generated as Shape Layers in Photoshop those Shape Layers can be output as vector content in some file formats (pdf and eps files), but within the layered Photshop image they will still be represented as pixels. 

Photoshop is a pixel oriented image editing program with limited vector capabilities. (Funnily enough in a few regards Illustrator's Path handling is inferior to Photoshop’s.)

Smart Object instances are pixels, no matter whether the Smart Object itself is a psd, psb, tif, jpg, eps, ai, pdf, … 

You can try pasting the copied Illustrator content as »Layers« – but depending on the illustration some features may not be reproduced as Shape Layers. 

Why did you create a svg and not an ai?