Notification badges tend to be red because red is the color that most attracts the human eye at a pre-attentive level (we are hard-wired to respond to red). Red things and motion will draw the eye in dramatic way, so use that power responsibly ;-)
Your badge needs to be considered in context of course... if your brand colors include a lot of red, or there are many other red things demanding attention on your page, then it might not have the desired effect.
The best practice is to do what will get the best results in supporting YOUR user's goals in YOUR context - ChatGPT can't know that. We use red badges in some places, especially when seeing those messages is the main point of the user being on that page, or they are time- or work-critical items. But since our branding colors DO include red, and because that count isn't always something the user needs to know urgently, there are places where blue is a better choice for us.
The best thing you can do is know your own requirements for the feature - How much does it need to stand out? What context is this appearing in for the user? How important are the things that are being notified about for the user? Is a badge count enough, or might stronger measures be needed? - and do some simple testing with your actual users to see what they respond to.