Epic: managed-overflow / second-bar redesign (modern menu-bar hiding)

Tracking epic for the single architectural change that resolves most of the open hiding bugs and feature asks at once.

## Why
Hidden Bar today hides icons by inflating an `NSStatusItem` separator's length so items fall off the left edge. That model has structural limits: macOS owns cross-app icon order (so new icons land hidden, with no API to reposition them), the always-hidden section is entangled with the separator state, the notch is just a narrow-bar variant of the same overflow problem, and macOS 27's menu-bar re-architecture can ignore the length entirely. A managed-overflow / second-bar approach (the model Bartender/Ice use) addresses all of these by managing presentation directly rather than relying on length inflation.

Design + options are written up in SPEC-003 (maintainer notes). This epic exists so the dependent issues are visible in one place; it is not a commitment to a specific implementation yet, the design decision comes first.

## Requirements this redesign must satisfy
- Keep user-chosen icons visible and persist that across relaunch (fixes the icon-order cluster).
- Hide always-hidden items based on the section being enabled, independent of the "hide separators" toggle; define recovery for items stuck off-screen.
- Work on notched displays and on macOS where length-inflation is ignored (graceful behavior, not silent breakage).

## Dependent issues

Second bar / sectioning / spillover asks:
#357 #148 #302 #174 #154 #229 #263 #341 #100 #107 #233 #232

Icon-order bugs (new/updated icons land hidden; positions not kept):
#28 #156 #181 #230 #231 #239 #252 #254 #275 #283 #321 #334

Always-hidden bugs:
#171 #224 #288 #242 #205

Notch overlap:
#206 #225 #228 #245 #267 #269 #280 #292 #330

macOS 26/27 hide breakage (long-term fix; near-term handled by diagnostics in #360):
#360 #327 #333

## Status
Design stage. Needs a product decision on scope and macOS 27 hardware to develop against. Closing this epic should close the dependent issues it delivers.