Is the following a scoping issue when trying to use Tee-Object - powershell

Question

Environment:
Windows Server 2016
Windows 10 Pro
PowerShell 5.1
$myVariable is empty, I think and I'm expecting there to be a string value.
Invoke-Command -ComputerName WKSP000D1E3F -Credential $creds -ScriptBlock {
sqlcmd -E -Q "select top 1 FirstName from customers" -d database1 -S "(localdb)\ProjectsV13" | Tee-Object -Variable myVariable
}
Write-Host $myVariable

Answer 1

Cpt.Whale has provided the crucial pointer in a comment: you fundamentally cannot set local variables from a script block being executed remotely (via Invoke-Command -ComputerName) - you must use output from the script block to communicate data back to the caller.
While you could apply Tee-Object locally instead (Invoke-Command ... | Tee-Object), there's a simpler solution, which works with all cmdlets, including cmdlet-like (advanced) functions and scripts:
Use the common -OutVariable (-ov) parameter to capture a cmdlet's output in a self-chosen variable while passing that output through:
# Note the `-OutVariable myVariable` part
# and that the variable name must be specified *without* a leading "$"
# Output is still being passed through.
Invoke-Command -OutVariable myVariable -ComputerName WKSP000D1E3F -Credential $creds -ScriptBlock {
sqlcmd -E -Q "select top 1 FirstName from customers" -d database1 -S "(localdb)\ProjectsV13"
}
# $myVariable now contains the captured content.
By contrast, if you want to capture output only, without also passing it through (to the display, by default), you can heed Santiago Squarzon's advice and simply assign the Invoke-Command call to your variable ($myVariable = Invoke-Command ...).
Notes re -OutVariable(-ov):
As shown above, and as shown with Tee-Object -Variable in your question, the name of the self-chosen target variable must be specified without a leading $, e.g. -OutVariable var, not Out-Variable $var; if you did the latter, the value of a preexisting $var variable (if defined) would be used as the variable name.
Unlike directly captured output, the target variable always receives array(-like) data, specifically, an instance of the System.Collections.ArrayList class - even if only one output object is present; e.g.:
# -> 'types: v1: String vs. v2: ArrayList'
$v1 = Write-Output -OutVariable v2 'one'
"types: v1: $($v1.GetType().Name) vs. v2: $($v2.GetType().Name)"
That is, while directly capturing output captures a single output object as-is, and multiple ones in a regular PowerShell array (of type [object[]], -OutVariable always creates an ArrayList - see GitHub issue #3154 for a discussion of this inconsistency.
With commands that do not support -OutVariable, namely simple scripts and functions as well as external programs:
To pass the output through in streaming fashion, i.e. as it becomes available, pipe to Tee-Object -Variable; e.g.:
# Passes output through as it is being emitted.
some.exe | Tee-Object -Variable myVariable
Otherwise - i.e. if it is acceptable to collect all output first, before passing it through - simply enclose an assignment statement in (...) to pass its value through - this approach performs better than Tee-Object -Variable; e.g.:
# Collects all output first, then passes it through.
($myVariable = some.exe)