Startup shell-integration reconcile unnecessarily starts all WSL distros

### Description of the new feature

Provide an option to probe base on usage-gated, not just profile-gated.

Every time Intelligent Terminal starts, it starts **all** installed WSL distributions — not just the ones the user has WSL tabs for. For WSL distros with `systemd` enabled (e.g. Podman WSL, Ubuntu with systemd), this means background services are permanently brought up on every Terminal launch, consuming memory and CPU indefinitely. The user never opened a WSL tab; they just launched PowerShell or any other non-WSL profile.

### Proposed technical implementation details

Options:

1. **Defer probing to first tab open**: only probe a WSL distro when the user actually opens a WSL tab. Install shell integration lazily on first use. This avoids the startup cost entirely for distros the user never opens.

2. **Registry-only identity resolution**: obtain `$WSL_DISTRO_NAME` from the registry (`HKCU\...\Lxss\\DistributionName`) without spawning `wsl.exe`. Defer `$HOME` resolution (the only thing that requires VM access) to first tab open or first UNC path access. This eliminates the VM boot on startup while preserving correctness.

3. **Persist probe cache across launches**: write the resolved `$WSL_DISTRO_NAME` / `$HOME` to a small state file so subsequent Terminal launches skip the probe for distros that were already resolved. This reduces the cost to one-time per distro per machine, not per process.

Option 1 or 2 would eliminate the unwanted WSL startup entirely. Option 3 would reduce it to a one-time cost.

Start by tracing the startup shell-integration reconcile path described in the issue and determine how it enumerates and probes WSL distributions. Compare the three proposed approaches with the maintainers, then verify that launching a non-WSL profile does not start unused distributions while WSL tabs still receive shell integration when opened.

Written by the indexing model from the issue text.