Texlive / LatexWorkshop - unable to Build or Preview Latex Files

I have installed TexLive on Ubuntu 20.04.1 LTS using

sudo apt-get install texlive

After this I created a file "text.tex" in Visual Studio Code. I installed the Plugin "Latex Workshop" and tried to preview or Build the .tex File.

I received the following error:

Recipe terminated with fatal error: spawn latexmk ENOENT.

According to this:

https://github.com/James-Yu/LaTeX-Workshop/issues/1742

The reason for this is, that something is wrong with the PATH Variable

I am not sure whether TexLive is actually included in my PATH:

Using echo $PATH yields:

/home/tony/.local/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/snap/bin:/opt/mssql-tools/bin

I can use latex-v and which latex yields:

/usr/bin/latex

TexLive itself is located at:

/usr/share/texlive

I have tried to debug this by following the advice from the github page – I copied the content of m PATH variable into the "env" fields in the settings.json of LatexWorkshop, however, the error persists.

Someone solved a fairly similar problem here:
How can I get VS Code LaTeX Workshop to choose the correct Latex distribution? This was on Windows however.

I am not sure whether something is wrong with my TexLive installation, my PATH variable or something is buggy or falsely set up within VSCode/LatexWorkshop.