docs: update UpdateManager and tests docs

Docs/ASLM/content/docs/ASLM/Services/UpdateManager.md

@@ -200,9 +200,46 @@ Saves one module manifest after update preferences changed in UI.
 
 ---
 
-#### `private static bool IsModuleAlreadyAtInstallTarget(ModuleConfig module, UpdateCandidate candidate)`
+#### `internal static bool HasRecordedRemoteSourceInstall(ModuleConfig module)`
 
-**Purpose:** ---
+**Purpose:** Returns whether the module manifest records a successful remote source install.
+
+**Parameters:**
+
+- `module`: The `ModuleConfig` to check.
+
+**Returns:** `true` if a remote source install is recorded; otherwise, `false`.
+
+**Example:**
+
+```csharp
+bool hasInstall = UpdateManager.HasRecordedRemoteSourceInstall(module);
+```
+
+---
+
+#### `internal static bool ShouldOfferReleaseInstallCandidate(ModuleConfig module, string resolvedReleaseTag)`
+
+**Purpose:** Returns whether a resolved release install candidate should be offered for download.
+
+**Parameters:**
+
+- `module`: The `ModuleConfig` to evaluate.
+- `resolvedReleaseTag`: The resolved release tag.
+
+**Returns:** `true` if the candidate should be offered; otherwise, `false`.
+
+**Example:**
+
+```csharp
+bool shouldOffer = UpdateManager.ShouldOfferReleaseInstallCandidate(module, "0.7.1.8");
+```
+
+---
+
+#### `internal static bool IsModuleAlreadyAtInstallTarget(ModuleConfig module, UpdateCandidate candidate)`
+
+**Purpose:** Returns whether the install candidate already matches the local installation (no file work needed).
 
 #### `private static string ResolveCurrentAppDisplayVersion()`
 

Docs/ASLM/content/docs/ASLM/Tests/Services/UpdateManagerInstallStateTests.md

@@ -0,0 +1,76 @@
+---
+title: "UpdateManagerInstallStateTests"
+draft: false
+---
+
+## Class `UpdateManagerInstallStateTests`
+
+`ASLM/Tests/Services/UpdateManagerInstallStateTests.cs` — tests `HasRecordedRemoteSourceInstall`, `ShouldOfferReleaseInstallCandidate`, and `IsModuleAlreadyAtInstallTarget` in [UpdateManager](../../Services/UpdateManager/) to verify update installation state checks.
+
+---
+
+## Test methods
+
+#### `public void HasRecordedRemoteSourceInstall_returns_false_for_release_module_without_installed_tag()`
+
+**Purpose:** Verifies that a release-tracked module without a recorded installed tag correctly returns false.
+
+---
+
+#### `public void HasRecordedRemoteSourceInstall_returns_true_when_installed_release_tag_is_set()`
+
+**Purpose:** Verifies that a release-tracked module with a recorded installed tag correctly returns true.
+
+---
+
+#### `public void HasRecordedRemoteSourceInstall_returns_false_for_branch_module_without_commit_sha()`
+
+**Purpose:** Verifies that a branch-tracked module without a recorded installed commit SHA correctly returns false.
+
+---
+
+#### `public void HasRecordedRemoteSourceInstall_returns_true_when_installed_commit_sha_is_set()`
+
+**Purpose:** Verifies that a branch-tracked module with a recorded installed commit SHA correctly returns true.
+
+---
+
+#### `public void ShouldOfferReleaseInstallCandidate_returns_true_when_version_matches_but_source_not_recorded()`
+
+**Purpose:** Verifies that an installation candidate should be offered if no remote source is recorded, even if the version matches.
+
+---
+
+#### `public void ShouldOfferReleaseInstallCandidate_returns_false_when_installed_release_tag_matches()`
+
+**Purpose:** Verifies that an installation candidate should not be offered when the local installed release tag perfectly matches the candidate.
+
+---
+
+#### `public void ShouldOfferReleaseInstallCandidate_returns_true_when_installed_release_tag_differs()`
+
+**Purpose:** Verifies that an installation candidate should be offered when the local installed release tag differs from the candidate.
+
+---
+
+#### `public void IsModuleAlreadyAtInstallTarget_returns_false_when_release_matches_but_source_not_recorded()`
+
+**Purpose:** Verifies that `IsModuleAlreadyAtInstallTarget` correctly returns false when the release matches but the source install isn't explicitly recorded.
+
+---
+
+#### `public void IsModuleAlreadyAtInstallTarget_returns_true_when_installed_release_tag_matches_candidate()`
+
+**Purpose:** Verifies that `IsModuleAlreadyAtInstallTarget` returns true when the installed release tag matches the update candidate.
+
+---
+
+#### `public void IsModuleAlreadyAtInstallTarget_returns_false_for_branch_when_installed_commit_sha_missing()`
+
+**Purpose:** Verifies that `IsModuleAlreadyAtInstallTarget` correctly returns false for a branch-tracked candidate when the installed commit SHA is missing.
+
+---
+
+## Related
+
+- [UpdateManager](../../Services/UpdateManager/)