Loading FixedPointNumbers invalidates ~7,700 precompiled method instances (7x slower first mtkcompile)

Summary

Loading FixedPointNumbers into a session that already has ModelingToolkit loaded invalidates
7,708 precompiled method instances and makes the first mtkcompile call take 23.59 s
instead of 0.04 s — a huge slowdown in a script that never uses a fixed-point number.

Most users meet this indirectly: ColorTypes/Colors depend on FixedPointNumbers, so any
Makie-based plotting next to ModelingToolkit pays this cost on the first model build.

MWE

# mwe.jl
using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
if get(ENV, "LOAD_FPN", "0") == "1"
    @eval using FixedPointNumbers      # <-- the only difference
end
@variables x(t)=1.0 y(t)=0.0
@named sys = System([D(x) ~ y, D(y) ~ -x], t)
t0 = time(); mtkcompile(sys); println("mtkcompile: ", round(time()-t0, digits=2), " s")

(test) pkg> st
Status `~/test/Project.toml`
  [53c48c17] FixedPointNumbers v0.9.1
  [961ee093] ModelingToolkit v11.41.0

$ julia --startup-file=no --project=. mwe.jl
mtkcompile: 0,04 s

$ LOAD_FPN=1 julia --startup-file=no --project=. mwe.jl
mtkcompile: 23.59 s

As a control, loading a package of comparable size that does not add methods to Base
generics (using LaTeXStrings) leaves the time unchanged at 0.04 s, so this is not the
general cost of loading a package.

Attribution

using SnoopCompileCore
using ModelingToolkit
invs = @snoop_invalidations using FixedPointNumbers;
using SnoopCompile
length(uinvalidated(invs))   # 7708, from 15 culprit methods

Ranked by countchildren:

None of these are type piracy — every one is dispatching on a FixedPointNumbers type. The
cost seems to come from adding methods to widely-inferred Base generics (promote_rule,
length, ceil, convert), which discards inference results in already-loaded packages
that call those generics on non-concrete argument types.

Question

Is there room to narrow any of these signatures, or is this something that has to be fixed
on the consuming side (or in Base)? I am mostly filing this for the record, since the
measured impact is large and I could not find an existing issue about it. Happy to run
further measurements if that helps.

Versions

Julia 1.12.7 (Linux, x86_64), FixedPointNumbers 0.8.6, ModelingToolkit 11.17.0,
SnoopCompile 3.2.9.

Comienza con mwe.jl y las mediciones de invalidaciones de SnoopCompile; después, inspecciona los métodos indicados en src/fixed.jl, src/normed.jl y src/FixedPointNumbers.jl. Compara firmas más específicas u otros cambios con respecto a las 7.708 invalidaciones y los tiempos de mtkcompile, comprobando al mismo tiempo que el comportamiento de FixedPointNumbers siga siendo correcto; el trabajo estará terminado cuando se reduzca el impacto de carga sin regresiones.