As far as I can see, when Godot imports SVGs it always converts them into a texture, they don't remain in vector graphics form.
The resolution of the texture (if you don't adjust the scale in the import panel) appears to be based on the width and height settings in the svg file.
You could either set a maximum resolution to use (the import panel's Size Limit setting) on the svgs, adjust the scale slider, or take a look inside of the file (open the svg file in a text editor) and look for a bit like this:
width="64" height="64"
and edit them to smaller values.
The default units (if not specified) for width and height in an svg are pixels.
The artist may have been working in real units, like that tree might be several meters tall. SVG has 1 inch equals 96 pixels, so saying an object is big will make the conversion generate massive resolutions.