Hi,
In my eyes the most important is that your layer#2 is really solid GND without other signals cutting the plnae into pieces.
The next important is that all your high frequency traces (for exact characteristic impedance) should be next to this GND_plane. (like layer#2 = GND, layer#1 = HF signals)
Whether layer#3 now contains extra GND often does not really matter, because this GND is split in pieces and thus rather high ohmic compared to the GND of layer#2.
If you are running low on layers, then better use layer#3 additionally for signal routing. The power supply traces just need to be wide enough not to drop too much (DC) voltage.
Here you need to focus on DC resistance only. The high frequency part for the power supplies are done via distributed decoupling capacitors with low impedance connections to the GND plane.
This is totally different when you need HF signals on both TOP and BOTTOM. But I guess this is not the case here.
And I think that part placement is more important than a second layer containing GND.
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I personally often use just one layer for GND. But this one is solid without any other signals.
Klaus