Hello Johannes, There is a method to get the entire thread with as many levels of replies as possible.
TwitterAPI is a python wrapper which has example code which does exactly this: https://github.com/geduldig/TwitterAPI/blob/master/examples/v2/conversation_tree.py
This will print out a tree with tweet_ids of the level 2,3,4 etc. You can just look up the tweets with a separate script.
A few things: You can straightaway replace the API keys you have into the script without worrying about the readfile() in the authentication (line 38, replace o.consumerkey with your key as a string etc.)
You should just be able to replace the conversation ID (this is different from tweet id) given in the script with one of the tweet you are mining replies to. If you don't know how to get the conversation id, you can follow steps 1-5 of my post and they will get you what you need. Hope this helps!