Put another way. When you buy a genuine BCR2 for a PS2 3V, or you follow many of the posts and guides to build one DIY, you notice we use 2 super capacitors in series each rated typically 2.5V-2.7V making the capacitor system capable of 5V to 5.4V roughly rated max, even though it's replacing a simple 2.4V rated nominal 2 cell battery pack.
Why? Because the PS2 3V charging circuit charges those capacitors or battery plugged into the board higher than 2.4V, so much so we don't dare depend on the single super capacitor rating of say at best 2.5-2.7V of typical single super capacitors.
So again, I KNOW for a fact 2.8V is both a valid and safe range, that the very charging circuit of PS2 3V boards easily reach that voltage, maybe even slightly higher when the battery is topped off.