[Bridges] change graph to favor Constraint bridges over Variable bridges

[odow]

x-ref jump-dev/ParametricOptInterface.jl#201 (comment)

• I need to change a bunch of the associated tests
• I need to run solver-tests.yml
  • https://github.com/jump-dev/MathOptInterface.jl/actions/runs/23575853864

I wonder if we should go further: should we use variable bridges iff we cannot do anything else? This would apply for CSDP and free variables, and ParameterToEqualTo. But not much else.

import MathOptInterface as MOI
using Clarabel
begin
    inner = MOI.instantiate(Clarabel.Optimizer; with_cache_type = Float64)
    model = MOI.Bridges.full_bridge_optimizer(inner, Float64)
    x, _ = MOI.add_constrained_variable(model, MOI.GreaterThan(1.0))
    MOI.Bridges.print_active_bridges(model)
    print(inner)
end

 * Supported objective: MOI.ScalarAffineFunction{Float64}
 * Unsupported constraint: MOI.VariableIndex-in-MOI.GreaterThan{Float64}
 |  bridged by:
 |   MOIB.Constraint.VectorizeBridge{Float64, MOI.VectorAffineFunction{Float64}, MOI.Nonnegatives, MOI.VariableIndex}
 |  may introduce:
 |   * Supported constraint: MOI.VectorAffineFunction{Float64}-in-MOI.Nonnegatives
Feasibility

Subject to:

VectorAffineFunction{Float64}-in-Nonnegatives
 ┌               ┐
 │-1.0 + 1.0 v[1]│
 └               ┘ ∈ Nonnegatives(1)