WSL fails with Wsl/ERROR_SERVICE_DOES_NOT_EXIST on all operations; also fails during InstallDistro after full reinstall

Nobody has claimed this yet.

## Summary
WSL fails with `Wsl/ERROR_SERVICE_DOES_NOT_EXIST` on every operation (`wsl --status`, `wsl -l -v`, launching a distro), and with `Wsl/InstallDistro/ERROR_SERVICE_DOES_NOT_EXIST` when attempting a fresh distro install after a full uninstall/reinstall.

This appears to be the same underlying issue as #13645 and #11882 (both open, no resolution posted), but I've done significantly deeper diagnosis that may help narrow it down.

## Environment
- Windows 11 Pro, build 10.0.22631.6199
- WSL client version: 2.7.14.0 (confirmed current via `wsl --update`)
- Kernel version: 6.1.83.2-2

## What I've ruled out
- **Not a stopped-service issue**: LxssManager, vmms, vmcompute, HvHost, StateRepository, RpcSs, RpcEptMapper, DcomLaunch, COMSysApp/EventSystem, AppXSvc, and ClipSVC were all confirmed running (many started manually) — error persists identically regardless.
- **Hyper-V hypervisor confirmed active** (`(Get-CimInstance Win32_ComputerSystem).HypervisorPresent` = True, `bcdedit` shows `hypervisorlaunchtype Auto`).
- **LxssManager COM/registry registration intact**: AppID `{e82567ae-2ea4-4dbc-bc68-8b0a0526d8d5}` and its CLSID `{4f476546-b412-4579-b64c-123df331e3d6}` are correctly registered; `LxssManager.dll` present and correctly referenced.
- **Full feature cycle performed**: `Disable-WindowsOptionalFeature` then `Enable-WindowsOptionalFeature` for both `Microsoft-Windows-Subsystem-Linux` and `VirtualMachinePlatform`, with a full restart between each step. No change.
- **Full uninstall/reinstall attempted**: Removed `CanonicalGroupLimited.Ubuntu` and `MicrosoftCorporationII.WindowsSubsystemForLinux` AppX packages, cleaned `HKCU\Software\Microsoft\Windows\CurrentVersion\Lxss`, then ran `wsl --install -d Ubuntu --web-download`. Failed at the `InstallDistro` step with the identical error.
- **`sfc /scannow`**: completed clean, no integrity violations.
- **`DISM /Online /Cleanup-Image /CheckHealth`**: no component store corruption.
- **Not a per-user-profile issue**: created a brand-new local admin account and ran `wsl --status` under that account's credentials via `Start-Process -Credential`. Identical failure — rules out profile-specific corruption.
- **Not domain/MDM managed** (`dsregcmd /status` shows AzureAdJoined/DomainJoined/EnterpriseJoined all NO), so not a policy restriction.
- **Windows Update is current**, nothing pending.
- One relevant System event around when this was first noticed: Hyper-V Virtual Machine Management service (vmms) crashed once with "Ran out of memory" shortly after a reboot, though vmms has run fine on manual starts since and the WSL error is unaffected either way.

## Repro
```
PS> wsl --status
The specified service does not exist as an installed service.
Error code: Wsl/ERROR_SERVICE_DOES_NOT_EXIST

PS> wsl --install -d Ubuntu --web-download
...
The specified service does not exist as an installed service.
Error code: Wsl/InstallDistro/ERROR_SERVICE_DOES_NOT_EXIST
```

## Logs
Collected via `collect-wsl-logs.ps1`. Happy to attach — the file is small (~40KB). Will follow up with a link once I've confirmed what's safe to post publicly (it includes registry exports and network config).

## Current impact
Existing Ubuntu WSL2 distro's disk image was manually backed up (raw `ext4.vhdx` copy, verified byte-for-byte) before troubleshooting further, so no data was lost, but WSL/Ubuntu are currently uninstalled on this machine pending a fix.

Start by reproducing the failures with `wsl --status` and `wsl --install -d Ubuntu --web-download`, then review the `collect-wsl-logs.ps1` output when it is attached. Done would mean identifying the cause of `Wsl/ERROR_SERVICE_DOES_NOT_EXIST` and defining an actionable fix; the issue currently does not point to a source file or test.

Written by the indexing model from the issue text.