Share option: How to append into text file? If I go to share in any app or from selected text (icon with three connected dots), I get some sharing options such as SMS, Bluetooth, WiFi direct, etc.

But I would also like to dump it directly into a chosen text file destination such as /(the default Android user directory path, different by each version)/Documents/Shared.txt

I need this for easily storing URLs into a file without needing to fumble and fiddle around with copying the URL bar and pasting it into a text editor, which costs a lot of time. The browser usually has a Share option.

Additionally, I would like it to be appended to the text file, not overwritten.
I am also fine if a new file is created each time, because some desktop PC commands can easily put 1000 tiny text files into 1 file, and Notepad++ and some Linux commands also support searching all files in a directory for text, even with regular expressions.
Simpletask does what you ask for. It creates a new line in a todo.txt file. 

Personally, I use Simpletask Cloudless and sync with syncthing. There is also Simpletask Nextcloud and Simpletask Dropbox. And if you like it, we should donate to the author (just found this amazing solution two days ago, so I didn't do it yet).