Conceptual considerations
Firstly, working out the "corresponding" side of the parcel polygon, for each side of the building polygon, is not trivial, especially using Geometry Generator. Finding the closest parcel side is easy, but these two are often not the same thing.
See the example in the image below, which shows the distance from each building side to the closest parcel side. The building edge highlighted red is "facing" south, but it will always be closer to the western parcel edge, which is what you see (distance of 1.19 m).
It is much more complicated to match up "south" (building edge) with "south" (parcel edge), and get that distance (shown with a red ? in the image). Even the centre of building edges may not match up with the parcel edge you want.
Minimum distance to each parcel edge (not building edge)
A more straightforward approach might be to calculate the minimum distance from each parcel edge to the building (so, kind of the inverse of what you asked for, which was from each building edge to the parcel, which was covered in the previous section). By accounting for each parcel edge, the results may be more useful in determining minimum setback compliance.
The image below shows an example:
You will notice some buildings have more than 4 "minimum distance" lines coming out of them - that's because the parcel technically has more than 4 sides (this is real-world data where parcel digitisation includes little irregular segments...).
Expressions
To achieve the above, make sure both your buildings and parcels layers are in the same projected CRS, then use this expression in Geometry Generator on your building layer (with Geometry type set to LineString / MultiLineString) - replace 'parcel' in the expression with the name of your parcel layer (case-sensitive).
collect_geometries(
array_foreach(
geometries_to_array(
overlay_within('parcel', -- set parcel layer name here
segments_to_lines(boundary($geometry)))[0]),
shortest_line($geometry,@element)
)
)
Under the geometry generator symbol, have a marker line symbol (on central point only), and use a font marker with the following expression under Character(s) - replace with ft as required:
round(length(geometry_n($geometry,@geometry_part_num)),2) || ' m'
The screenshot below shows what the setup should look like (geometry generator, simple line, and marker line with font marker) and shows where to use the expression above (yellow circle):
To fix the orientation of the font marker, follow the instructions under point 4 of this answer showing how to get polygon side dimensions.
You need to use a font marker to show distance, not labels, because while you can place a label in a geometry-generated position, the label engine has no way of accessing the properties (i.e., length) of each generated geometry (see discussion under the aforementioned answer).
Variations
Centre of parcel edge instead of vertex
You will notice that minimum distances above are drawn from a building vertex to a parcel vertex - that's because that will generally be the technically closest distance, geometrically.
You can get a prettier result by drawing the shortest line from the centre of each parcel side to the building by replacing shortest_line($geometry,@element) with shortest_line($geometry,centroid(@element)) in the geometry generator expression, which will look like this:
But this only looks nicer; it will no longer show the actual closest setback distance so please bear this in mind when assessing compliance.
Exclude small parcel segments
To avoid the "messy" look with irregularly drawn parcels, you can filter out parcel edges that are under a certain length, thus only getting building setbacks from "major" parcel edges. Use the expression below for geometry generator and set the minimum length as desired (here, only parcel edges 5 m and above are included).
collect_geometries(
array_foreach(
array_filter(
geometries_to_array(
overlay_within('parcel', -- set parcel layer name here
segments_to_lines(boundary($geometry)))[0]),
length(@element) >= 5), -- set minimum parcel edge length here
shortest_line($geometry,@element)
)
)
Example with parcel edges 5 m and above filtered out (blue arrows):
