Repairing the hole is easy,matching paint can be a challenge for handymen , diyers and less competent painters.

Get a factory touch up kit. You ill need or want one over time anyway.

"Easy"? Strip and start again. That looks deeper than paint. If you want it unnoticeable it is not a DIY.

You don’t need someone skilled and you certainly don’t need to strip it. You just need a touch up kit with a resin wax filler (which most have). The wood will cure the wax by drawing the moisture in.

After that, the only people who are going to spot the defect are people looking hard for defects and those same people would have found defects in the coating before this even happened.