Constructing the tree is where parent links, chief positions and number
ranges get wired up wrongly without anyone noticing — a team under the wrong
Bereich looks perfectly plausible in the org chart. So the construction is a
pure function taking an id generator, and the checks that matter are asserted
rather than eyeballed: exactly one root, every unit's parent of the expected
type, every unit reaching the root, one chief position per unit, unique
numbers in the right ranges, and every position pointing at a real unit and
a real job.
Also introduces the job catalogue this model needs. job_title was free text
per person, so "Schlosser:in" and "Schlosser" could coexist and no breakdown
by occupation was possible; jobs are now deduplicated by title and shared
across positions.
Every Abteilung gets a chief position, which is the level the old three-table
model had no room for.
Correction to the previous commit message: it claimed the cut-over could
follow later while the old tables kept working. It cannot. The legacy
resolve_manager_for() finds a Bereichsleitung by "division_id = X and
team_id is null and org_level = 1", and an Abteilungsleitung satisfies the
same predicate — its LIMIT 1 would then pick one of the two arbitrarily. The
two models cannot both be correct once the new level is populated, so the
remaining work is a single cut across the 11 RPCs that read the legacy
columns, not a gradual migration.
