Make sure you get a laptop with a modern Ryzen processor since the battery life (and performance on battery) is often a lot better than Intel. There are a lot out there that fit the bill like Lenovo’s yoga/ideapad lineup. Just be weary of two things:

• Some 14" laptops may have soldered RAM or SSDs making them impossible to upgrade
• Don’t go off of processor names, they’re often pretty misleading. For example a Ryzen 7 7730U is significantly worse than a Ryzen 7 7840U.

Not many suggestions seem to be forthcoming and the laptops I have are outside of your budget or bought at a time when medium range laptops were cheaper. Your budget is unfortunately below what the linux laptop vendors I know ship. So, to narrow down your parameters:

• Go for AMD --> less to no issues with Linux
  • will most likely be an “APU” (CPU with integrated graphics) which are OK-ish for gaming --> check https://www.notebookcheck.net/ for the APU you find and ensure your game or an equivalent can be played with it
• 16GB is nearly too little (depending on what you do) so try to get 32GB
• Use https://linux-hardware.org/?view=search_computer to check how compatible your choice is with linux
• 500GB SSD is kinda standard, but as a dev downloading whatever dependencies or compiling, aim for higher (1TB should be enough)

Edit: Why does your gaming laptop have to be replaced? Hardware issues? Often those are quite good for programming.