Return value in powershell script stored in string not utf8

Question

I'm trying to extract tables out of a pdf using tabula and powershell. When I enter the command directly in the powershell console, I get the expected result displayed (in utf8 with umlaut-symbols)

java -jar "./tabula-java/$tabulaVersion" --spreadsheet -a 114,53,180,556 "./table.pdf"

But when I put it in a string variable and then write to a file the umlaut symbols become gibberish

$text = java -jar "./tabula-1.0.1-jar-with-dependencies.jar" --spreadsheet -a 114,53,180,556 "./table.pdf"   
Set-Content -Path "./file.txt" -Value $text

Even if I print the variable in the console, the umlaut-symbols are not properly displayed

$text = java -jar "./tabula-1.0.1-jar-with-dependencies.jar" --spreadsheet -a 114,53,180,556 "./table.pdf"   
Write-Output $text  

Is there a way to store it in a string variable (and therefore being able to manipulate the content) and write it to a file with keeping the utf8 (without BOM) encoding?

Using the approach from https://stackoverflow.com/a/5596984/1786528 does not work for me either

$Utf8NoBomEncoding = New-Object System.Text.UTF8Encoding $False
[System.IO.File]::WriteAllLines($filepath, $text, $Utf8NoBomEncoding)

I don't get an error, but also no file is created or line added.

Update:

[System.IO.File]::WriteAllLines creates a file (in UTF without BOM), I just used a relative path and did not set [System.Environment]::CurrentDirectory = (Get-Location).Path. But nonetheless are the umlaut-symbols not correct.

Additional details

case 1: output directly in console, e.g.

java -jar "./tabula-1.0.1-jar-with-dependencies.jar" --spreadsheet "./table.pdf" 

case 2: output stored in variable, then printed in console, e.g.

$text = java -jar "./tabula-1.0.1-jar-with-dependencies.jar" --spreadsheet "./table.pdf"   
Write-Output $text 

case 3: output stored in variable but with -D"file.encoding=UTF-8", then printed in console, e.g.

$text = java -D"file.encoding=UTF-8" -jar "./tabula-1.0.1-jar-with-dependencies.jar" --spreadsheet "./table.pdf"   
Write-Output $text 

Update:

$OutputEncoding = US-ASCII and [System.Console]::OutputEncoding = OEM United States (IBM437)

case 4: output directly in console (with changing [System.Console]::OutputEncoding beforehand), e.g.

[System.Console]::OutputEncoding = System.Text.Encoding]::GetEncoding(1252)
java -jar "./tabula-1.0.1-jar-with-dependencies.jar" --spreadsheet "./table.pdf" 

case 5: output stored in variable, then printed in console (with changing [System.Console]::OutputEncoding beforehand), e.g.

[System.Console]::OutputEncoding = System.Text.Encoding]::GetEncoding(1252)
$text = java -jar "./tabula-1.0.1-jar-with-dependencies.jar" --spreadsheet "./table.pdf"   
Write-Output $text 

This will result in this for umlaut symbols

pdf    case 1    case 2     case 3    case 4     case 5
 ä      ä         Σ          ├ñ        „          ä
 ö      ö         ÷          ├╢        ”          ö
 ü      ü         ⁿ          ├╝                  ü