Option 1:
To modify the topology, you need to use GRASS -> v.clean from Processing toolbox -> GRASS -> Vector -> v.clean, and in the cleaning tool use Break, as you can see below:
After cleaning the polygon, you may need to delete the duplicate geometries. It can be done using the tool Delete duplicate geometries from QGIS Processing Toolbox -> QGIS -> Vector general tools -> Delete duplicate geometries
You may need to re-enter the values in the attribute table after cleaning your polygon shapefile.
Option 2:
Another approach is to use Select by Expression (attribute) to select every year and save it as a separate shapefile, then use the Union tool to combine them again. The Union tool will clean the polygons and preserve the information in the attribute table.
Option 3:
Using Select by Expression (attribute) to select every year and save it as a separate shapefile, then use the Difference tool to remove the previous year's polygons using the newer year's polygons then merge them again using the Merge tool, and so on. It is less efficient compared to the Union tool but can do the job.