Increase floor area ratio by purchasing green land?

If the meadow is not building land, then clearly no.

Talk to the municipality about whether you are allowed to combine the plots and have part of it converted into building land ... but that will certainly take time. I don't think the municipality will decide that for you in a hurry. It is a longer process and the outcome is uncertain.

We have the opportunity to purchase a piece of meadow in the undeveloped outer area, which directly adjoins our property in the unplanned inner area. Would the purchase also change the calculation basis for the floor space index?

Nevertheless, you should acquire the land because of its strategic location, incorporate it into your property and initially use it as garden land. When the day comes, you are prepared....