AFAIK when the tab/window is closed/truely hidden (when the tab isn't directly visible in a browser window) credits just stop incrementing since arena is defined OFF.
I never minimize a browser window (constantly working with 3 different browsers - Vivaldi as main, then Chromium, finally Firefox for easier Godot compatibility) on 5 virtual desktops, I just move it to an other virtual desktop, eventually hibernating tabs if needed.
As I told, I'm using multiple virtual desktops to keep the tab/window active even if it's not visible to prevent CPU/GPU overheat (yes, your game is an heavy resource consumer on light configs, especially on CPU+G chipset resources when the game is visible).
About your game, the lacking of "true" idling is concerning: the complete lack of progression in arena and credits gain when the tab is hidden/window is closed (maybe when minimized too) is slowing everything since the main tool is gaining credits to gain diamonds to earn an higher multiplier after a rebirth. TBF, I've seen warnings about "browsers' recent tech is the cause of issues with idling" for over a decade and still, lots of devs have managed to find an hack :) I'm pretty sure you will too ^^
/poke: can you really ask your customers to keep your prog visible at any time to progress?
I wish arena wouldn't be depending on the game's ON/OFF status :P
Below, this PC's config (I may not be part of your primary target!):
Host: OptiPlex 7010 01 // CPU: Intel i5-3570S (4) @ 3.800GHz
GPU: Intel HD Graphics
RAM: 7828MiB (+ 8Go SWAP)
Primary HDD: Crucial RealSSD P400 256 Go
OS: MX-23.6_x64 Libretto (Kernel: Linux 6.1.38-2)
8 or 16-bits like aesthetics have been tricking me for years -_-" these games keep getting heavier.