When I first installed and later updated this bucket through scoop, I got this error message:

The term: init-spicetify-config-and-apply.ps1 is not recognized as a name of a cmdlet, function, script ...

Basically it's not in path, and failed the rest of the installation process.

It seems that all the scripts from this bucket's scripts folder are not copied into where spicetify-cli is installed. I did a manually fix by copying all scripts into where it's needed, but each update is troublesome. So I submit a new issue.
This error may happened because there is another bucket (main) which also contains spicetify-cli, and this line in your spicetify-cli:

      "installer": {
        "script": [
            "...",
            "$null, $bucket = find_manifest($app)", <---
            "$bucketdir = Find-BucketDirectory($bucket)",
           "...", 
        ]
      } 

Without find_manifest($app, $bucket) specifying which bucket, it's set to default as main bucket, whose script folder does not contains necessary scripts like init-spicetify-config-and-apply.ps1, spicetify-apply.ps1, ... and the following line

    @(all the scripts) | ForEach-Object { Copy-Item "..." } ;

fail, never made it into spicetify-cli installation directory.
I suggest changing that line into

    "$null, $bucket = find_manifest $app 'spotify'",

as

     find_manifest($app, 'spotify'),

both will be passed as array into $app param.
I'm sorry for the verbosity, hope this help anyone who encounter the same problem as I did.