feat(stats): a capture records which encoder and GPU produced it

The stage split is the thing an fps-shortfall report is diagnosed from, and
it cannot be read without knowing the backend behind it: a p50 `submit` of
10 ms means "the GPU's CSC+encode throughput is the ceiling" on one backend
and something else entirely on another. The capture's meta carried the mode,
codec and client but neither the encoder nor the GPU, so every report so far
cost a round-trip asking which one it was.

Both come from `pf_gpu::active()` — the record the encoder open itself
writes — so they name the branch that really opened rather than a re-derived
guess that goes stale the moment a backend gains an internal fallback. Read
once per capture, not per frame.

The console shows them next to the mode in the recording's header. Both
fields are `serde(default)`, so a recording made before this still loads and
simply omits them.

Refs #9

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

api/openapi.json

@@ -3912,11 +3912,19 @@
             "format": "int64",
             "minimum": 0
           },
+          "encoder_backend": {
+            "type": "string",
+            "description": "The encode backend that ACTUALLY opened for this session — `\"nvenc\"`, `\"vaapi\"`,\n`\"vulkan\"`, `\"amf\"`, `\"qsv\"`, `\"software\"`, … — and the GPU it runs on.\n\nRecorded because the stage split alone can't be read without them. A p50 `submit` of 10 ms\nmeans \"the GPU's CSC+encode throughput is the ceiling\" on one backend and something else\nentirely on another, and every fps-shortfall report so far has cost a round-trip asking\nwhich one it was. Both come from `pf_gpu::active()`, the record the encoder open itself\nwrites, so they name the branch that really opened rather than a re-derived guess.\n\n`\"\"` when nothing was streaming at registration (or on a build without the record)."
+          },
           "fps": {
             "type": "integer",
             "format": "int32",
             "minimum": 0
           },
+          "gpu": {
+            "type": "string",
+            "description": "Human-readable GPU name (`\"NVIDIA GeForce RTX 4090\"`, `\"CPU (openh264)\"`), or `\"\"`."
+          },
           "height": {
             "type": "integer",
             "format": "int32",