I'm actually going to be replacing the backend with react but it's in development ! Absolutely a valid point and wordpress should never be a long term goal indeed. I'm just one man right now! Maybe someday with a team I could have produced it from scratch rapidly
WordPress is already good but the script you are using right now is not what users will feel like a chat site
There are a lot of premium WordPress chat script and plugin if you want to continue using WordPress this is a list of the best script and plugins
The cheapest is $11 a month and the premium one is worth $40 a month.
https://quadlayers.com/best-wordpress-group-chat-plugins/