Good video. A few things I think are worth mentioning. First, Dialogic is Emi's project who is executive director of Godot Foundation. So chances are high this add on won't be forgotten to be updated. Second, Dialogic seems to be have a lot more features than Dialogue Manager at this point. For simple dialogues either would work. For more elaborated games or for a all in one solution despite being in alpha, I'd pick Dialogic.
I think a bigger feature for us is to be able to import from a CSV file exported from something like Google Sheets or Excel. It's very important for us that our team members do not need to familiarize themselves with a new tool just to add some text in the game. Google Sheets or Excel is something that everyone in the team already knows so being able to simply setup the template file and have them work on it without needing to fuss over the editor is a huge plus for us.
I tried to use Ink It is possible to get working in Godot, but it is far easier to use with Unity. I do not recommend it over DialogueManager as they both function and write very similarly but dialogue manager is leagues easier to get working in Godot. But if you ever want to taste Unity for a lil bit Inky is well worth trying