Continue the background wipe across every output

[sven-strothoff]

Stacked on #10660. The first two commits here are that PR; the change in
this one is the last two. Once #10660 lands this diff reduces to those.
Draft until then.

The wipe is the thing that made me stop and look the first time I changed a
theme on Omarchy. It isn't a crossfade and it isn't a swap — it's a tilted
front that opens out of the middle of the screen and pushes the old
wallpaper off both edges. It reads as one deliberate gesture, and it makes
changing a theme feel like an event rather than a settings change.

On a single screen it is perfect. On two, the illusion breaks: each output
opens its own front at its own centre, so instead of one gesture you get
two unrelated ones firing simultaneously, and the effect collapses back
into "the wallpaper changed."

This makes the layout the stage instead of the individual output. The front
starts at the centre of the output you were working on when you changed the
wallpaper or theme, and keeps going onto the others — arriving from
whichever edge faces the output you started on, at the vertical offset your
layout implies. What was two competing animations becomes one front
crossing the desk, which is what the effect was always reaching for. It's a
small change to what the mask is measured against and the whole thing
scales up to however many screens you own.

Three things worth calling out about how it behaves:

It starts where you are. The origin is the output Hyprland has focused
when the change is made, snapshotted at the start of the transition so
moving focus mid-wipe can't drag it. Change your theme on the laptop and
the front opens there and travels out to the external; do it on the
external and it goes the other way. The wipe begins where your attention
already is, which is the whole reason it works on one screen.

It honours your physical layout. All of it is done in Hyprland's own
layout coordinates, so a stacked, offset, mismatched-height or
mismatched-resolution arrangement is followed rather than approximated —
including a gap, where the front spends a moment crossing the space
between two outputs, exactly as it would if the desk were one surface. The
flip side is the obvious one: it is only as right as your layout is. If
your outputs are not arranged in monitors.lua the way they physically
sit on your desk, the front will cross them in the order the compositor
believes in, not the order you see. That is arguably a feature — it gives
you an immediate, visible reason to fix your layout.

It preserves the original on the output it starts from. The mask
geometry reduces algebraically to the existing single-screen formula for
the origin output, so nothing about the effect you already know changes on
the screen you triggered it from. The other outputs are the continuation
that was previously missing. Single-monitor setups are unaffected.

Configuration

Both the behaviour and the timing are configurable, read the same way the
idle service reads its own keys:

key	values	default
background.transition	layout, output	layout
background.transitionDuration	milliseconds	derived from the layout

output restores the previous per-output wipe, and reproduces its geometry
exactly rather than approximating it. Unset or unrecognised values fall
back to the defaults.

I'd argue for the defaults as they stand. layout is the point of the
change, and the per-output behaviour is the thing this fixes rather than a
taste people are likely to hold. The derived duration matters more:
covering a much longer path in the original 420ms makes the front move
several times faster than it does today, which on my layout turned the
wipe into something closer to a flicker. So the duration scales with how
much further the front actually has to travel, keeping the edge at roughly
the speed it has on one screen.

That scaling is capped at 900ms, and the cap is the one number here I hold
loosely. Constant edge velocity on my two outputs wants about 1180ms,
which felt long enough to notice as waiting; 900ms keeps it a gesture. On
a three- or four-output wall the cap will bind harder and the front will
move faster than it does on one screen — a deliberate trade against a
transition that overstays. Happy to change either number, or drop the cap
and let velocity stay constant, if you'd rather.

Verification

The geometry is checked against three invariants, over eight layouts
(aligned, offset, gapped, stacked, secondary-on-the-left, negative
coordinates, three outputs with mixed offsets, and a portrait secondary),
for every choice of origin in each:

1. the front is continuous across outputs — a panel's local front plus its
   screen.x equals the global front at that y, exactly
2. at revealProgress == 1 the mask covers every output completely,
   densely sampled down each output's height rather than only at corners
3. the origin output reduces exactly to the untouched single-screen formula

All hold. I also compared the numbers the running shell computes against an
independent implementation of the same formulas, for both origin choices on
my hardware — originX/originY, per-output dx, originDy, centerTop,
centerBottom, reach and duration all match to floating point.

Configuration was exercised end to end through shell.json: default,
transition=output, a pinned duration, both together, and deliberately
invalid values. transition=output reproduces the original geometry
exactly (centerTop 1335.0, centerBottom 1065.0, reach 1339 on my
internal panel, which is what the pre-change expression gives).

Two limits on that, stated plainly. My machine runs 4.0.2, whose shell
predates Ui/BackgroundMedia.qml, so quattro's Background.qml will not
load here — I verified against the 4.0.2 copy with the same edits applied,
as in #10660. And hyprmoncfgd owns my display layout and reapplies it
over monitors.lua, so I could not rearrange my outputs to test the
alignments on real hardware; the eight layouts above are verified at the
formula level, and only one real two-output arrangement (side by side,
748px vertical offset, different heights and resolutions) was exercised
live, in both origin directions.

./test/all fails the same 5 of 234 files as quattro does on this
machine with the patch reverted, and no others: config-test.sh,
snapper-test.sh and unowned-system-paths-test.sh want an omarchy-pkgs
checkout I don't have, locate-test.sh dies in a UnicodeDecodeError in
its own helper, and runtime-smoke-test.sh trips #9975's per-screen
IpcHandler assertion. config-test.sh output is byte-identical to the
base-commit run, so the new background.* keys don't disturb it.

Setup: Hyprland, eDP-1 at 0,748 (2400x1500 logical) and DP-12 at 2400,0
(2400x1350 logical), both at scale 1.6.

[sven-strothoff]

Raised as a suggestion for discussion too, per contributing.md: #10678 — happy to keep the design conversation there and leave this PR for the code.