Also works on Windows 10, native, 22H2 (10.0.19045.4780).

Also Works on Windows 11 24H2.

Is posible to check if previously exists other ID and increment without removing previous one?

Here is my bit. It do it incremental

function Register-EventScript {
    param (
        [string] $eventToRegister, # Either Startup or Shutdown
        [string] $pathToScript,
        [string] $scriptParameters
    )
    $path = "$ENV:systemRoot\System32\GroupPolicy\Machine\Scripts\$eventToRegister"
    if (-not (Test-Path $path)) {
        # Path must exist for this to work
        New-Item -Path $path -ItemType Directory -Force
    }

    # Define base registry paths
    $baseRegPaths = @(
        "HKLM:\SOFTWARE\Microsoft\Windows\CurrentVersion\Group Policy\Scripts\$eventToRegister",
        "HKLM:\SOFTWARE\Microsoft\Windows\CurrentVersion\Group Policy\State\Machine\Scripts\$eventToRegister"
    )

    # Find the next available index for the script
    $index = 0
    foreach ($basePath in $baseRegPaths) {
        $existingKeys = Get-ChildItem -Path $basePath -ErrorAction SilentlyContinue | Where-Object { $_.PSChildName -match '^\d+$' } | Select-Object -ExpandProperty PSChildName
        if ($existingKeys) {
            $maxIndex = ($existingKeys | ForEach-Object { [int]$_ } | Measure-Object -Maximum).Maximum
            $index = [math]::Max($index, $maxIndex + 1)
        }
    }

    # Create registry paths with the new index
    $regPaths = $baseRegPaths | ForEach-Object { "$_\$index" }
    $scriptRegPaths = $baseRegPaths | ForEach-Object { "$_\$index\0" }

    # Create registry keys for the new index
    foreach ($regPath in $regPaths) {
        if (-not (Test-Path $regPath)) {
            New-Item -Path $regPath -Force
        }
        # Set properties for the parent key
        New-ItemProperty -Path $regPath -Name DisplayName -PropertyType String -Value "Local Group Policy" -Force
        New-ItemProperty -Path $regPath -Name FileSysPath -PropertyType String -Value "$ENV:systemRoot\System32\GroupPolicy\Machine" -Force
        New-ItemProperty -Path $regPath -Name GPO-ID -PropertyType String -Value "LocalGPO" -Force
        New-ItemProperty -Path $regPath -Name GPOName -PropertyType String -Value "Local Group Policy" -Force
        New-ItemProperty -Path $regPath -Name PSScriptOrder -PropertyType DWord -Value 2 -Force
        New-ItemProperty -Path $regPath -Name SOM-ID -PropertyType String -Value "Local" -Force
    }

    # Create subkeys and set properties for the script
    foreach ($scriptRegPath in $scriptRegPaths) {
        if (-not (Test-Path $scriptRegPath)) {
            New-Item -Path $scriptRegPath -Force
        }
        New-ItemProperty -Path $scriptRegPath -Name Script -PropertyType String -Value $pathToScript -Force
        New-ItemProperty -Path $scriptRegPath -Name Parameters -PropertyType String -Value $scriptParameters -Force
        New-ItemProperty -Path $scriptRegPath -Name IsPowershell -PropertyType DWord -Value 1 -Force
        New-ItemProperty -Path $scriptRegPath -Name ExecTime -PropertyType QWord -Value 0 -Force
    }
}

# get crrentlocation so we can form the full path to the script to register
$currentLocation = $PSScriptRoot

Register-EventScript -eventToRegister "Startup" -pathToScript "$currentLocation\ScriptToRun.ps1" -scriptParameters "Startup"
Register-EventScript -eventToRegister "Shutdown" -pathToScript "$currentLocation\ScriptToRun.ps1" -scriptParameters "Shutdown"

And this is for unregister:

function Unregister-EventScript {
    param (
        [string] $eventToUnregister # Either Startup or Shutdown
    )

    # Base registry paths where scripts are registered
    $baseRegPaths = @(
        "HKLM:\SOFTWARE\Microsoft\Windows\CurrentVersion\Group Policy\Scripts\${eventToUnregister}",
        "HKLM:\SOFTWARE\Microsoft\Windows\CurrentVersion\Group Policy\State\Machine\Scripts\${eventToUnregister}"
    )

    # Collect all registered scripts
    $scripts = @()
    foreach ($basePath in $baseRegPaths) {
        if (Test-Path $basePath) {
            Get-ChildItem -Path $basePath -ErrorAction SilentlyContinue | ForEach-Object {
                $index = $_.PSChildName
                $scriptPath = (Get-ItemProperty -Path "$basePath\$index\0" -ErrorAction SilentlyContinue).Script
                $params     = (Get-ItemProperty -Path "$basePath\$index\0" -ErrorAction SilentlyContinue).Parameters

                if ($scriptPath) {
                    $scripts += [PSCustomObject]@{
                        Event      = $eventToUnregister
                        Index      = $index
                        ScriptPath = $scriptPath
                        Parameters = $params
                        RegBase    = $basePath
                    }
                }
            }
        }
    }

    if (-not $scripts) {
        Write-Host "No scripts found for ${eventToUnregister}"
        return
    }

    # Show scripts and ask the user which ones to remove
    Write-Host "`nScripts found for event ${eventToUnregister}:`n"
    $i = 0
    $scripts | ForEach-Object {
        Write-Host "[$i] $($_.ScriptPath) $($_.Parameters)"
        $i++
    }

    $selection = Read-Host "Enter the number of the script to remove (comma-separated for multiple, or 'all' for all)"
    if ($selection -eq "all") {
        $toRemove = $scripts
    }
    else {
        $indexes = $selection -split "," | ForEach-Object { $_.Trim() } | Where-Object { $_ -match '^\d+$' }
        $toRemove = $scripts[$indexes]
    }

    # Remove selected scripts
    foreach ($s in $toRemove) {
        $regPath = "$($s.RegBase)\$($s.Index)"
        if (Test-Path $regPath) {
            Remove-Item -Path $regPath -Recurse -Force
            Write-Host "Removed: $($s.ScriptPath) [${eventToUnregister}]"
        }
    }
}

# Example usage:
Unregister-EventScript -eventToUnregister "Startup"
Unregister-EventScript -eventToUnregister "Shutdown"