Or a blurry png icon like the second one.
I want to know in what situations they will appear correspondingly?
And is there a way to customize the icon below? My understanding is that this site is missing because I can see the corresponding .miss file for the domain name in “data/icon_cache”.
The first one in your picture will be shown for login items by the client for example if you don’t have a host set while the latter 
will be used when the server can’t or won’t find a requested icon for a hostname or as a fallback image by the client if the server call fails.
Yes, it’s most likely possible. You can manually place icons for individual hosts:
If you want to change the default that is not easily possible because the image is embedded into the binary so you would have to recompile Vaultwarden with a replaced fallback image (and while I think it’s unlikely that the request would fail also the web-vault to be sure).
