Model's print summary should include value type

[odow]

There's nothing to indicate that this is a GenericModel{BigFloat}:

julia> using JuMP

julia> file = joinpath(dirname(dirname(pathof(MOI))), "test", "FileFormats", "SDPA", "models", "example_A.dat-s")
"/Users/oscar/.julia/packages/MathOptInterface/2CULs/test/FileFormats/SDPA/models/example_A.dat-s"

julia> model = open(file, "r") do io
           return read(
               io,
               GenericModel{BigFloat};
               format = MOI.FileFormats.FORMAT_SDPA,
               number_type = BigFloat,
           )
       end
A JuMP Model
Minimization problem with:
Variables: 2
Objective function type: GenericAffExpr{BigFloat, GenericVariableRef{BigFloat}}
`Vector{GenericAffExpr{BigFloat, GenericVariableRef{BigFloat}}}`-in-`MathOptInterface.PositiveSemidefiniteConeTriangle`: 2 constraints
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.

[odow]

How about something like:

julia> model
A JuMP Model
├ objective_sense: MIN_SENSE
│ └ objective_function_type: AffExpr
├ num_variables: 1
├ num_constraints: 2
│ ├ VariableRef in MOI.GreaterThan{Float64}: 1
│ └ VariableRef in MOI.Integer: 1
├ backend
│ ├ mode: AUTOMATIC
│ ├ solver_name: HiGHS
│ └ value_type: Float64
└ registered names
  └ :x

[blegat]

I like it, we could also say if there is a bridge layer and if there are any bridge in bridge_type (we can say nothing if bridge_type is empty

[odow]

So I wondered about this. There's merit to showing all of backend(model). But this makes it too big.

What about adding something like ├ backend: call `backend(model)` for more information

[odow]

Bridges and caching optimizer and stuff is too complicated for general users.

Maybe we have just:

julia> model
A JuMP Model
├ value_type: Float64
├ objective_sense: MIN_SENSE
│ └ objective_function_type: AffExpr
├ num_variables: 1
├ num_constraints: 2
│ ├ VariableRef in MOI.GreaterThan{Float64}: 1
│ └ VariableRef in MOI.Integer: 1
└ registered names
  └ :x

[blegat]

We don't want to show all information but the bridge layer is a keyword argument to JuMP.Model we have JuMP.add_bridge so I thought we might add these too.
Not showing the backend at all as in your last comment is nice, the user can do backend(model) to see more. We could also omit value_type if it's Float64

[odow]

See #3803.

For the bridges: I wonder if some mix of backend(model) and print_active_bridges(model) is enough. The bridges are irrelevant for new users.