So, I've figured out a way for this chatbot to work. It was a hassle, but it's usable.
To make the experience smooth, you've got to make the dialogues always include the speaking character's name. It should be automatic, but in case ai forgets, edit the response, please.
Second: character ai deals okay with a single character present in the conversation. But if you are in a situation when there's more than one, character ai has some issues with providing responses from multiple characters, unlike Moemate. Therefore, to get more people engaged in dialogue before you, the player, speak; you should simply write a dot. "." just a single dot and in my testing the character spoken to would pick up the dialogue.
That's all the instructions I've got so far! I hope you'll enjoy this version as much as you enjoyed the Moemate counterpart :3
CharacterAI:
https://character.ai/chat/7eq5DZGbEpszge_e2rW9XMVJ7AeVN5oFSsj68jHnUss
SakuraAI:
https://www.sakura.fm/chat/rPU8VCk