In your escritura the boundaries should be defined and therefore your surveyor can use these to confirm the real area.
The Land Registry should accept a correction to the area in an Escritura but you may have to check exactly what back up, other than the surveyor’s report, it may need to register the new area. You should also make sure the surveyor is a member of the relevant “Colegio”.
With regard to the Ayuntamiento, obviously no one can predict what they may do but since your neighbours will presumably have been paying taxes for the additional land which may be yours then the Ayuntamiento should be OK. It could be that your neighbours try to get a rebate on overpaid taxes but how likely that is I’ve no idea. You should also check with the Ayuntamiento what documentation they would need to register with the catastral office any new area but once this is all done and you have a certificate from the Land Registry showing an area of 10.000m2 or more then you are perfectly entitled to aplly for a segregation licence from the Ayuntamiento thereby splitting the land into 2 individual plots.
The catastral office would presumably reassess your plots for future taxes.
Hope this helps