Generate list of neighboring polygons QGIS

Question

I am looking for a way to create a list of polygons that each polygon touches. I am a complete novice at QGIS and I have no idea where to even start. I am using a map of voting precincts in Utah that looks like this:

I want to generate a list that shows the precinct name (the attribute is called PrecinctID). Preferably, the output list would be in the form of a CSV file. How would I accomplish this?

Edit: When following the instructions provided by PieterB, I get an empty error window. The Python error log reads:

Traceback (most recent call last):
              File "/Applications/QGIS3.app/Contents/MacOS/../Resources/python/plugins/db_manager/db_plugins/gpkg/data_model.py", line 63, in run
              self.model = GPKGSqlResultModel(self.db, self.sql, None)
              File "/Applications/QGIS3.app/Contents/MacOS/../Resources/python/plugins/db_manager/db_plugins/data_model.py", line 195, in __init__
              c = self.db._execute(None, sql)
              File "/Applications/QGIS3.app/Contents/MacOS/../Resources/python/plugins/db_manager/db_plugins/gpkg/connector.py", line 147, in _execute
              self.connection = spatialite_connect(str(self.dbname))
              File "/Applications/QGIS3.app/Contents/MacOS/../Resources/python/qgis/utils.py", line 595, in spatialite_connect
              con.enable_load_extension(True)
             AttributeError: 'sqlite3.Connection' object has no attribute 'enable_load_extension'

Answer 1

You can do this in QGIS with SQL.

Go to Database > DB-manager > Virtual Layers > Project Layers

Open the SQL-window and add following code. Change 'layername' twice to the appropriate layername:

select a."PrecinctID",  group_concat(b."PrecinctID") as neighbours
from layername a, layername b
where touches(a.geometry, b.geometry)
group by a."PrecinctID"

• Check 'load as a new layer'
• Uncheck 'Geometry column'
• Give a layer name
• click load

Now you get a table which you can save (right-click > save as) as a .csv

It will take a while before the results are computed. Depending on how your features are stored, it can go faster when you put them in a database (eg. geopackage) and set an index on the geometry and PrecinctID.

Importing your data into geopackage:

• right click your layer and choose Export > Save features as
• choose Geopackage
• give your file and layer a name

As everything goes fine, the layer will be loaded in QGIS.

After that, open DB-manager and connect to your geopackage (right clik on 'geopackage' > New connection)

Now you have to make some indexes:

• a spatial index like explained here: https://gis.stackexchange.com/a/265574/7849

• an index on PrecinctID: in DB-manager select you layer and go to Table > Edit Table.
  

• Open the tab 'Index' and click on 'Add index', select PrecinctID in the dropdownlist.

In geopackage the geometry is called 'geom'. So you have to adapt the code a little bit:

select a."PrecinctID",  group_concat(b."PrecinctID") as neighbours
from layername a, layername b
where touches(a.geom, b.geom)
group by a."PrecinctID"