What I would actually do, in order:
- Lift the dried surface film while it is still a film. Emulsion that has dried on the surface peels or lifts in sheets and that removes most of the material in ten minutes. Do this before it rains again and breaks up.
- Skim the top 5-10cm of the patch itself, a bit wider than the stain. A bucket or two of soil.
- Dispose of it properly: that is household waste for the tip, not the compost heap and not the green bin. Take the tins too; the tip will have a paint stream.
- Backfill with compost or topsoil and leave it.
What I would not do is dig deeply or treat it as a remediation project. Going deeper spreads it and disturbs soil structure for no gain, given how shallow the contamination is.