chore: move to Python 3.14 and Alpine 3.24

Both Docker stages now use python:3.14-alpine3.24. Since there is no
combined uv image tag for python3.14-alpine3.24, the static uv binary is
copied from ghcr.io/astral-sh/uv:0.13.1 into the builder stage. Requires
Python 3.14, refreshes uv.lock, and updates the README badges.

Dockerfile

@@ -1,9 +1,10 @@
 # syntax=docker/dockerfile:1
 
 # ---- Build stage -------------------------------------------------------------
-# Uses the uv image to resolve and install the pinned dependency set into a
-# self-contained virtual environment.
-FROM ghcr.io/astral-sh/uv:python3.13-alpine3.23 AS builder
+# Python 3.14 / Alpine 3.24 base. uv is copied from its official image because
+# there is no combined python3.14-alpine3.24 uv image tag.
+FROM python:3.14-alpine3.24 AS builder
+COPY --from=ghcr.io/astral-sh/uv:0.13.1 /uv /uvx /bin/
 
 ENV UV_COMPILE_BYTECODE=1 \
     UV_LINK_MODE=copy \
@@ -23,7 +24,7 @@ RUN --mount=type=cache,target=/root/.cache/uv \
     uv sync --frozen --no-dev --no-editable
 
 # ---- Runtime stage -----------------------------------------------------------
-FROM python:3.13-alpine3.23 AS runtime
+FROM python:3.14-alpine3.24 AS runtime
 
 ENV PYTHONDONTWRITEBYTECODE=1 \
     PYTHONUNBUFFERED=1 \