Public/Get-LocalInstance.ps1

function Get-LocalInstance {

    <#
 
    .SYNOPSIS
    Returns connection parameters to a available localDb.
 
    .DESCRIPTION
    Uses [SqlLocalDB Utility](https://docs.microsoft.com/en-us/sql/tools/sqllocaldb-utility?view=sql-server-ver15) to get info about the available local db.
 
    .EXAMPLE
    PS> Get-SqlTestLocalInstance
 
    [PSCustomObject]
 
    Name Value
    ---- -----
    DataSource (LocalDb)\MSSQLLocalDB
    ConnectionString Data Source=(LocalDb)\MSSQLLocalDB;Integrated Security=True
    Version v11.0
 
    #>


    [CmdletBinding()]
    param ()

    Import-Module PsSqlLocalDb -ErrorAction Stop

    $instance = Get-LocalDbInstance

    [PSCustomObject] @{
        ConnectionString = "Data Source=(LocalDb)\$( $instance.Name );Connect Timeout=30;Integrated Security=True"
        DataSource       = "(LocalDb)\$( $instance.Name )"
        ConnectTimeout   = 30
        Version          = $instance.Version
    } | Write-Output
}