Loading GeometryBasics invalidates ~11,000 precompiled method instances (7x slower first mtkcompile)

Summary

Loading GeometryBasics into a session that already has ModelingToolkit loaded invalidates
11,182 precompiled method instances and makes the first mtkcompile call take
15.8 s instead of 2.2 s — a 7x slowdown in a script that never uses a geometric type.

Most users meet this indirectly: Makie depends on GeometryBasics, 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_GB", "0") == "1"
    @eval using GeometryBasics        # <-- 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")

$ julia --startup-file=no --project=. mwe.jl
mtkcompile: 2.22 s

$ LOAD_GB=1 julia --startup-file=no --project=. mwe.jl
mtkcompile: 15.80 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 2.23 s, so this is not the
general cost of loading a package.

Attribution

using SnoopCompileCore
using ModelingToolkit
invs = @snoop_invalidations using GeometryBasics;
using SnoopCompile
length(uinvalidated(invs))   # 11182, from 169 culprit methods

Ranked by countchildren:

Nearly all of it comes from OffsetInteger. convert(::Type{IT}, ::OffsetInteger) where IT<:Integer in particular is a method on Base.convert whose second argument carries the
package's own type but whose first is a broad Type{IT<:Integer}, which discards inference
results in already-loaded packages that call convert(::Type{<:Integer}, x) on
non-concrete argument types.

Question

Is OffsetInteger still load-bearing, and if so, is there room to narrow these signatures?
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), GeometryBasics 0.5.12, ModelingToolkit 11.17.0,
SnoopCompile 3.2.9.

Start with the MWE in the issue and reproduce the mtkcompile timings with and without GeometryBasics. Inspect the OffsetInteger methods in src/offsetintegers.jl, especially lines 53, 55, 81, 85, and 87, and use the SnoopCompile commands shown to measure invalidations. Done means establishing whether these methods are load-bearing and documenting or implementing a narrower signature with comparable regression measurements.