refactor(net): own live session composition

Extract reset, selection, entered-world, and route construction behind LiveSessionHost while preserving the sole LiveSessionController authority. Retain partial route and subscription cleanup for retry, and replace the embedded ACE-only shortcut with the exact named-retail unsigned skill formula.

Co-authored-by: Codex <codex@openai.com>

docs/research/skill_formula_calculate_pseudocode.md

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+# Retail skill-formula calculation
+
+## Oracle
+
+- Named retail: `SkillFormula::Calculate @ 0x00591960` in
+  `named-retail/acclient_2013_pseudo_c.txt`.
+- Retail layout: `SkillFormula` in `named-retail/acclient.h:40199` stores six
+  unsigned 32-bit fields in wire order: `W`, `X`, `Y`, `Z`, `Attr1`, `Attr2`.
+
+The signed-looking branches in the recovered x87 code are not signed formula
+semantics. They are the compiler's unsigned-32-bit-to-floating-point fix-up:
+when the high bit is set, it adds `2^32` after the initial signed conversion.
+
+## Pseudocode
+
+```text
+bool SkillFormula.Calculate(uint attribute1, uint attribute2, out uint result)
+{
+    uint divisor = Z;
+    if (divisor == 0)
+        return false;
+
+    // Every operation on this line is uint32 and wraps modulo 2^32.
+    uint numerator = X * attribute1 + Y * attribute2 + W;
+
+    // Formula values are non-negative. Retail rounds to nearest integer,
+    // with exact halves rounding upward.
+    result = uint(floor(double(numerator) / double(divisor) + 0.5));
+    return true;
+}
+```
+
+Consequences pinned by the port:
+
+- `Z == 0` is the only failure gate. `X == 0` remains a valid formula.
+- `W` participates in the numerator before division; it is not added after
+  division.
+- multiplication and addition wrap as unsigned 32-bit arithmetic before the
+  floating-point division.
+- the division rounds half-up; it does not truncate.
+
+## Reference cross-check
+
+ACE's [`SkillFormula`](https://github.com/ACEmulator/ACE/blob/master/Source/ACE.DatLoader/Entity/SkillFormula.cs)
+confirms the unsigned DAT order `W, X, Y, Z, Attr1, Attr2`. ACE's
+[`AttributeFormula.GetFormula`](https://github.com/ACEmulator/ACE/blob/master/Source/ACE.Server/Entity/AttributeFormula.cs)
+is only an interpretation aid: it rejects `X == 0`, assumes unit multipliers,
+omits `W`, and rounds a summed-attribute quotient. That is sufficient for
+ordinary stock ACE data but is not the general retail algorithm.
+
+Chorizite DatReaderWriter's generated
+[`SkillFormula`](https://github.com/Chorizite/DatReaderWriter/blob/master/DatReaderWriter/Generated/Types/SkillFormula.generated.cs)
+independently confirms the same six-field order and maps its public names to
+`W`, `X`, `Y`, and `Z`. It exposes the four arithmetic words as signed `int`,
+so the retail port must reinterpret their bits as `uint`. Its summary places
+the additive value after division; the named retail function proves that the
+actual client adds `W` to the numerator instead.
+
+## Port decision
+
+`RetailSkillFormula` is the sole App-layer calculation seam. It reinterprets
+the DAT words as unsigned, performs the exact unchecked 32-bit numerator, and
+uses the retail half-up division. `LiveSkillCreditResolver` performs only the
+skill-table lookup and treats a missing attribute as zero, matching the prior
+live-property projection behavior.