Sites depicting 360 images usually use this approach of loading first a low resolution version of the panorama (to shortening the time for the user) and later loading the full resolution version.
The fact that some areas are shown blured is due to using a mechanism for slicing the 360 image into smaller pieces, so the snapshot is showing a moment when the lower version (blured) was already loaded and some of the final images starting to show up. This usually translate to “Multiresolution” panorama, i.e. sets of images at different sizes, where level 0 is the blured version, and level 1, 2 and so on are loaded as the user zooms in.
Theeejs does not provide this kind of mechanism out-of-the-box, as its not in the ‘3d realm’ (for a lack of a better term). If you plan to use mostly 360 images and/or not fully use 3d features at all,you can consider using a dedicated 360 library like Pannellum.js, you can se here the example demostrating this approach.
Eventually you could try combining a library like that with threejs, or extracting the basic logic and applying that to your application.