How to use interacting PostgreSQL/PostGIS triggers in QGIS to create multiple labels on polygons?

EDIT:

The trigger functions posted are well done but there are still a few issues. I've uploaded two screen recordings:

http://workupload.com/file/ygRnYtp9

http://workupload.com/file/OBY7i9Fh

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I use point geometries (table 'label_point') to place multiple labels on polygon geometries (table 'soil'). After doing layer edits I've to update the affected label_point features. Therefore I've created a trigger function.

CREATE TABLE label_point (
gid serial NOT NULL,
geom geometry(point, SRID),
label_sample varchar(255),
CONSTRAINT label_point_pkey PRIMARY KEY (gid)
);

CREATE TABLE soil (
gid serial NOT NULL,
geom geometry(polygon, SRID),

label varchar(255),
CONSTRAINT soil_pkey PRIMARY KEY (gid)
);

CREATE OR REPLACE FUNCTION sample_label()
RETURNS trigger AS $body$
    BEGIN
    IF GeometryType(NEW.geom) = 'POINT' THEN
        EXECUTE 'SELECT label FROM soil WHERE ST_Within($1, soil.geom) LIMIT 1'
        USING NEW.geom 

        INTO NEW.label_sample;
        RETURN NEW;
    ELSEIF GeometryType(NEW.geom) = 'POLYGON' THEN
        EXECUTE 'UPDATE label_point SET label_sample = NULL WHERE ST_Within(label_point.geom, $1)'
        USING NEW.geom;
        RETURN NEW;
    END IF;
    END;
$body$ LANGUAGE plpgsql;


CREATE TRIGGER tg_sample_label BEFORE INSERT OR UPDATE
ON label_point FOR EACH ROW
EXECUTE PROCEDURE sample_label();


CREATE TRIGGER tg_sample_label AFTER INSERT OR UPDATE
ON soil FOR EACH ROW
EXECUTE PROCEDURE sample_label();

Unfortunately this solution suffers from two issues.

1.) When deleting a soil feature or moving a soil feature (ST_Within(label_point.geom, soil.geom) = FALSE) the sample_point features are not updated to NULL.

2.) When splitting a soil feature using the QGIS 'Split Feature Tool' and changing the label of one polygon part the label_point features are not updated proberly after saving the edits.

Can anyone help me with this?