Definitely buy it. That way you keep distance and prevent the municipality from eventually designating it as a building area. We also have such a case, and we paid significantly more than 5€/sqm (but it's only 132sqm, and we had to buy the forest as well). But keep in mind - forest is forest. That means you are not allowed to fence it in, build anything on it, damage it, and may only plant typical forest plants (for us, local deciduous trees, pine, a few shrubs, blueberries). Still - such a patch of nature right next to the garden border is great! Although - from what I see, your forest is a pine plantation. I would prospectively supplement and, in the (very) long term, replace it with something sustainable, that is, deciduous trees.
