"I'll let you go" implies that they are discourteously keeping you from other things you need to be doing. They may use it even if they feel like you are keeping them from things they need to be doing.
"I have to go" can be a bit abrupt, but it is common and idiomatic, especially in online conversations.
Both of those phrases are used when someone realises they need to go and want to cut off the conversation.
"I'm gonna head out" is very informal and idiomatic. It sounds natural in an informal context with a friend. It implies you can't chat anymore because you are physically going to travel somewhere else.
"Good chat! gotta go now"
"Thanks for the chat! See you next time?" Or a specific time if that makes sense.
"Thank you I don't need anything else" If you are chatting with a customer service rep.
I think many people are also fine just dropping an online conversation without saying any good-bye words, depending on the context.