Best way to transfer data from old Android to new one without losing apps?

Just got a shiny new Android phone and I'm trying to move everything over from my old device. I want to keep all my apps, settings, and data intact without having to redownload and set everything up manually. I've tried using Google's backup feature, but it seems hit or miss - some apps don't restore properly, and I'm worried about losing saved game progress or chat histories.

Has anyone found a reliable way to do a full data transfer between Android phones? Are there any third-party apps or tools that work better than the built-in options? Would love to hear your experiences or tips so I don't have to spend hours configuring my new phone.

Also, any advice on what to watch out for during the transfer to avoid common pitfalls?