Edit "search result webpart" > click "Change query".
In "Query text" type path to your list/library
Path:"https://.../Lists/testList/" (contentclass:STS_ListItem OR IsDocument:True)
Check if your Managed Properties are (Query Retrieve Refine Sort Safe) like OOTB refinable managed properties.
It requires custom solutions to build a tree view web part in SharePoint. Please see the references here:
Tree View WebPart for Sharepoint List Data.
Sharepoint 2013 : Tree view structure for Document library and setting permissions.
There are also third-party solutions that provide this function, for example:
SharePoint Tree View - Bamboo Solutions Web ...
Since you're using Spfx, why are you using JSOM? You should be using sphttp service and even better PnP JS for your tasks. Those libraries Wil handle the asynchronous calls for you, and Spfx provides you with the context already so you don't have to initialize context through JSOM.