Convert HHmm to Fallout game-hour float

Add parsing and application of HHmm time strings as Fallout game-hour floats so GUI time presets apply correctly. Introduce ParseHHmmToGameHour in plugin/src/F4TWorldStateSync.cpp and use it when building the console command (formats as set gamehour to <float> with fallback to the raw HHmm string if parsing fails). Improve logging to indicate when a parsed HHmm was used. Update protocol/server-world-state.md, changelog.md, and docs/dev-log.md to document the behavior and rationale.

docs/dev-log.md

@@ -9,6 +9,36 @@ failed experiments, successful tests, and next steps.
 
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+## 2026-06-24 - Convert `HHmm` Time to Game-Hour Float
+
+### Summary
+Fixed server GUI time presets applying the wrong time in Fallout 4 by converting `HHmm` values (such as `2200`) to game-hour float values before running `set gamehour`.
+
+### Files Changed
+- `plugin/src/F4TWorldStateSync.cpp`
+- `protocol/server-world-state.md`
+- `changelog.md`
+
+### Details
+- `serverWorldState.timeHHmm` is now parsed as `HHmm` on the client.
+- Parsed times are applied as float hours:
+  - `2200` -> `22.0`
+  - `1830` -> `18.5`
+- If parsing fails, plugin falls back to the original raw command for compatibility.
+
+### Testing
+- Not re-tested in-game in this session.
+- User reported `Night (2200)` previously set daytime while console showed `set gamehour to 2200`.
+- Recommended: test `0600`, `1200`, `1900`, and `2200` from GUI and verify resulting in-game time.
+
+### Known Issues
+- None currently known.
+
+### Next Steps
+- Rebuild plugin and verify each time preset maps correctly in-game.
+
+---
+
 ## 2026-06-24 - Replace Invalid GUI Weather IDs
 
 ### Summary