Enumerate only the immediate contract folders, then build the matching sibling destination from each folder's name. The -Recurse on $temp_path is what includes the old contracts tree and its nested folders.

For copying the files directly inside each contract folder into the matching sibling's Documents folder:

$root = 'C:\Users\Documents\script'
$source = Join-Path $root 'contracts'

Get-ChildItem -LiteralPath $source -Directory | ForEach-Object {
    $destination = Join-Path (Join-Path $root $_.Name) 'Documents'
    New-Item -ItemType Directory -Path $destination -Force | Out-Null
    Get-ChildItem -LiteralPath $_.FullName -File | ForEach-Object {
        Copy-Item -LiteralPath $_.FullName -Destination $destination -WhatIf
    }
}

Review the -WhatIf output, then remove -WhatIf to perform the copies. This leaves the original files in place and does not descend into nested subfolders. I tested the copy operation on PowerShell 7.6.5 with two contract numbers: both went to the corresponding sibling Documents directories, and no Documents directory was created inside contracts. Existing files with the same name in a destination can be overwritten by Copy-Item.

See Get-ChildItem -Directory/-File and Copy-Item -WhatIf.

Your comment says #Move files from Parent to Destination folder

But you use Copy-File. Do you actually want to move them or is copy sufficient?

In the general case I would not recommend moving a file out of a directory while it is being enumerated, no matter the computer language or scripting system.

The safest strategy is to build a list of the files you want to move, then once happy with the list and completed all directory scanning to then move the files either en-mass or individually to the appropriate place.