Rename the DEM-construction NoiseModel to say it is a parameter set, not a simulator noise model

[ciaranra]

Problem

pecos.qec.surface.NoiseModel collides conceptually with the simulator-side noise
models while being a different kind of object:

name	what it is
GeneralNoiseModel / DepolarizingNoiseModel (via general_noise(), depolarizing_noise())	executable models that apply noise during simulation; fluent Rust-backed builders, 47 and 7 with_* methods
pecos.qec.surface.NoiseModel	a parameter bag consumed at DEM construction; a Python dataclass, 30 fields plus derived properties

The confusion is live rather than theoretical: docs/workflows/guppy-dem-decoding.md
now imports NoiseModel from pecos.qec.surface in a section that also discusses
simulator noise, and since #422 this dataclass is the shared idle-noise vocabulary for
both the Guppy and native-surface DEM routes — so it is no longer a surface-code detail
either.

NoiseParameters (or similar) would say what it is.

Two separable questions

1. The rename. ~240 references across ~34 files (source, tests, docs, examples).
   Public, so it needs an alias plus a deprecation ramp rather than a hard rename —
   same discipline as Deprecation ramp: align pecos-engines GeneralNoiseModel idle-noise API with the structured vocabulary #424.
2. Whether it should gain with_* setters to mirror general_noise(). Recommend
   no: it is a dataclass, so dataclasses.replace(params, p1=...) already provides
   what .with_p1(...) would, and 30 setters would restate the field list a third time
   (fields, docstring, methods) with three places to drift. The conveniences that earn
   their place already exist: uniform(), is_noiseless, physical_error_rate,
   for_runtime_idle_time_units().

Note for whoever picks this up: a "user-facing uses bare setters, low-level uses
with_*" rule does not hold in this repo. sim()'s noise builders are user-facing
and use with_*; the Rust-backed BpOsdBuilder uses bare. The convention is genuinely
inconsistent, so a naming decision here should be made deliberately rather than by
appeal to an existing rule.

Why this belongs with #425

#425 already covers aligning the non-idle GeneralNoiseModel surfaces with the
structured vocabulary. The DEM-side and engines-side names should be settled once,
together — otherwise this gets renamed to NoiseParameters now and possibly again
when the unified vocabulary lands. Deliberately kept out of PR #420 for that reason,
and because a 240-site public rename mixed into a large functional PR is hard to review.

Related: #422 (which made this dataclass the shared idle vocabulary), #424, #425.

[ciaranra]

Decision (2026-08-04): rename to NoiseParameters and give it the with_* fluent interface matching the sim() noise builders.

This supersedes my earlier recommendation in the issue body against adding setters. The reasoning that changes it: the goal is not to save typing over dataclasses.replace — it is that DEM-side and simulator-side noise configuration should look the same, since users move between them constantly and (since #422) this object is already the shared idle-noise vocabulary.

Target shape, mirroring general_noise() / depolarizing_noise():

noise = (
    NoiseParameters()
    .with_p1_probability(0.002)
    .with_p2_probability(0.02)
    .with_meas_probability(0.02)
    .with_prep_probability(0.02)
    .with_p_idle_linear_rate(0.01)
)
dem_build = DetectorErrorModel.builder().program(prog).qubits(7).noise(noise).build()

Design points to settle during implementation:

• Method names should match the sim-side spellings where the concept is the same (with_p1_probability, with_p2_probability, with_meas_probability, with_prep_probability, and the with_p_idle_* family). Where they differ today, that difference is itself worth a look — matching names is most of the value.
• No terminal method, matching the sim noise builders, which are passed directly into .noise(...) rather than .build()-ed.
• Keep the dataclass constructor working. NoiseParameters(p1=..., p2=...) must stay valid; the fluent form is additive. The existing derived helpers (uniform(), is_noiseless, physical_error_rate, for_runtime_idle_time_units()) stay.
• The structured idle families and their normalization must survive unchanged — __post_init__ translates the families into per-axis fields and then clears them, which is load-bearing for the dataclasses.replace round-trip in for_runtime_idle_time_units() (see Port the structured idle-noise families to the native-surface NoiseModel (twirl/threshold route) #422).
• NoiseModel remains as a deprecated alias through a ramp, as in Deprecation ramp: align pecos-engines GeneralNoiseModel idle-noise API with the structured vocabulary #424.

Scope: ~240 references across ~34 files, so this lands as its own PR rather than inside #420. It should be sequenced with #425, where the engines-side names are settled, so the two sides converge once rather than twice.