Follow up #143: share hive state and protect nested repair handoffs

[Marcus Ferreira (mvaferreira)]

Why this follow-up exists

#143 merged as 1b2a597 while the additional #146/#147 review fixes were being validated.
This PR contains only the shared-foundation changes those reviews need; it does not alter the
approved/merged #143 history.

File	Change
OfflineRepairCommon.ps1	Shared writable-hive depth/file bindings and default Windows drive; persistent nested-VM ownership marker and a reentrant cross-process lifecycle mutex
Get-OfflineWindowsDisk.ps1	Publishes the shared default; refuses active managed/unrelated guests before disk preparation; limits automatic shutdown to ProblemVM or an explicit custom Id
README.md	Documents strict writers, persistent rollback records and verified guest hand-offs

No scenario or map.json entry is added. #146 and #147 use this shared contract; consuming
scenario PRs must wait until all three outstanding helper changes have merged.

Registry state across dot-source scopes

Set-OfflineWindowsDrive binds the selected root and publishes the default through
Get-OfflineRepairState. Scope-private variables are no longer independent sources of truth.
The same state owns hive depth and active file bindings, preventing an inner callback from
unloading its outer caller's hive or silently switching the file/default underneath it.

Nested-guest coordination

Discovery previously turned off every running Hyper-V guest. It now fails before any disk
preparation when another guest is active or #147's helper has marked a guest as managed. It does
not merely skip that guest and attempt to online its disk.

The persistent repair-script-library:nested-repair:v1 Notes line works across PowerShell
processes. A shared mutex serializes ownership/start/stop and disk-preparation transitions.
The owning flow must explicitly call Stop-NestedRepairVmGraceful, confirm Stopped, and
then rediscover the disk. Automatic unmanaged shutdown uses an exact VM object and verifies Off;
no wildcard-name shutdown or success-shaped enumeration failure remains.

Validation and limits

• Existing 120/120 defect and 53/53 follow-up cases pass on PS5.1 and PS7.
• Dedicated registry regressions pass 140/140 on both engines; PSScriptAnalyzer is zero
  across all eight helper files.
• 87/87 nested lifecycle cases pass on both engines, including cross-process mutex exclusion.
• 33 native assertions on a disposable VHD verify discovery/default-drive binding, real
  writable synthetic hives, strict selected-set writes, cross-scope calls and unwind/cleanup.
• 93 native Hyper-V assertions use disposable Gen1/Gen2 guests with actual passthrough VHD
  disks. Fresh-process discovery refuses to interrupt them; disk return is verified. Five
  original guests and seven original disks remain unchanged.
• The test guests are firmware-only and the hives are synthetic. These results are not
  presented as Windows guest boot/payload validation or a fresh --preview scenario matrix.

Local test tooling stays outside the contribution, as requested. No protection was disabled,
and no existing lab guest or original disk was repurposed for these checks.

[Marcus Ferreira (mvaferreira)]

Closing this extra split to keep the review work in the two existing open PRs, #146 and #147. The tested shared-helper changes will be folded into those PRs; merged #143 remains unchanged. The branch is retained while that integration is completed.