Dear @latrache,
Thank you for reaching out to us again!
I came up with the following information during my research: with a Duldung, you are not allowed to travel abroad. Your stay is limited to Germany. Within Germany, travelling freely is allowed. However, there are some Duldungen, where the stay/ residence is spatially limited. The limitation would be noted in your Duldung.
"Auslandsreisen sind nicht gestattet, der Aufenthalt ist grundsätzlich auf den Bereich Deutschlands beschränkt. In Deutschland kann man frei reisen. Achtung: Es gibt auch Duldungen, bei denen der Aufenthalt räumlich beschränkt ist. Dies ist in der jeweiligen Duldung vermerkt."
Source: https://***.nds-fluerat.org/wp-content/uploads/2018/08/Erlaubnis-von-Reisen-je-nach-Aufenthaltstitel-oder-papier.pdf
I'm unsure if the note in your Duldung, that you have to reside in Kaarst, applies to your travels, too. To be sure, it would probably be best to check with the responsible authority.
I hope this information helps a bit. Let us know if you have any further questions.
Best regards,
Isa