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If we subtract the damage, we have good remaining wood of 2.65mm

Even though, we would steam some of this dent out, which  may improve the measurements, it still has to be flat sanded smooth which means more wood needs to come off.

I would not repaint this guitar.

For me to repaint it, I have minimum tolerances, Cedar minimum 2.9mm of wood with no finish on it and 2.6mm Spruce with no finish. The manufacturer of this Lowden had a very nice light top at 2.9mm with no finish applied, so that IMO is very thin to start with.
What happens when a guitars top is too thin.

Here is a Cole Clark that had been refinished without the above concerns given, the top was 2.4mm thick in places and made from spruce which is stiffer than Cedar.

The Border around the guitar has dipped in under tension, you can see the whole top tearing itself away from the sides

This guitar needed the top replaced
P3
Turning that into info, the good parts of the guitar, have a finish of 0.2mm so remaining good wood is 2.89mm
"How To" Measure Acoustic Top