Signal and power integrity - 4 layer board
Have a ground plane. You don't need a power plane. You do need a low impedance power supply at each IC, which means stitching as many decoupling caps as required, per supply, per IC, close enough to the ICs, directly between power and ground.

Power planes are great when you have a single plane, lots of ICs using it, and want to spread out the decoupling caps. It's a total waste of a layer if those don't apply. With multiple rails, any attempt to put all the power distribution on a single layer, that you then hopefully call the power plane, will result in silly polygons that are simply wide tracks. It's much easier to route and to nail with decoupling if you simply treat it all as tracks, on the most appropriate layer, from the start.

All the return currents will flow in the ground plane. Keep the ground plane as a plane, do not cut it into a lace curtain to route other tracks on that layer (that can happen when there isn't an organised way to route tracks, and the last track or two has to cut through the ground plane)

There is a technique called Manhattan routing, which will allow you to organise point to point or mesh routing on just two layers, without tripping yourself up. Choose an east-west layer, and a north-south layer. Hop between them using vias. While you lay the board out, resist the temptation to put a sneaky track running EW on the NS layer, and vice versa, you will regret it later when you need to cross tracks.

That gives you the spare 4th layer for signal routing the signals that wouldn't fit on the Manhattan layers.