Problem with MTK's BifurcationKit extension

[TorkelE]

Would be useful to get advice on what is failing here. MWE below. This also stops Catalyst's BifurcationKit extension from working, making it a blocker for a potential Catalyst release.

using ModelingToolkitBase
using ModelingToolkitBase: t_nounits as t, D_nounits as D
using BifurcationKit

@variables X1(t) X2(t)
@parameters k1 k2 Γ = missing [guess = 1.0] 
eqs = [
    0 ~ -k1*X1 + k2*(-X1 + Γ)
    0 ~ X2 + X1 - Γ
]
@mtkcompile sys = System(eqs)

u0_bif = [X1 => 1.0, X2 => 1.0]
ps = [k1 => 1.0, k2 => 1.0]
bif_par = k1
p_span = (0.2, 5.0)
BifurcationProblem(sys, u0_bif, ps, bif_par)

ERROR: Initial condition underdefined. Some are missing from the variable map.
Please provide a default (`u0`), initialization equation, or guess
for the following variables:

Γ

Stacktrace:
 [1] varmap_to_vars(varmap::Dict{…}, vars::Vector{…}; tofloat::Bool, use_union::Bool, container_type::Type, buffer_eltype::Type, toterm::Function, check::Bool, allow_symbolic::Bool, is_initializeprob::Bool, substitution_limit::Int64, missing_values::ModelingToolkitBase.MissingGuessValue.var"typeof(MissingGuessValue)")
   @ ModelingToolkitBase C:\Users\Torkel\.julia\dev\ModelingToolkit\lib\ModelingToolkitBase\src\systems\problem_utils.jl:355
 [2] varmap_to_vars
   @ C:\Users\Torkel\.julia\dev\ModelingToolkit\lib\ModelingToolkitBase\src\systems\problem_utils.jl:314 [inlined]
 [3] BifurcationProblem(::System, ::Vector{…}, ::Vector{…}, ::Num; plot_var::Nothing, record_from_solution::Function, jac::Bool, kwargs::@Kwargs{})
   @ MTKBifurcationKitExt C:\Users\Torkel\.julia\dev\ModelingToolkit\lib\ModelingToolkitBase\ext\MTKBifurcationKitExt.jl:138
 [4] BifurcationProblem(::System, ::Vector{Pair{Num, Float64}}, ::Vector{Pair{Num, Float64}}, ::Num)
   @ MTKBifurcationKitExt C:\Users\Torkel\.julia\dev\ModelingToolkit\lib\ModelingToolkitBase\ext\MTKBifurcationKitExt.jl:99
 [5] top-level scope
   @ c:\Users\Torkel\Desktop\Julia\Julia Playground\Environment - Catalyst Test (full)\catalyst_tests_playground.jl:17
Some type information was truncated. Use `show(err)` to see complete types.

[AayushSabharwal]

This one is a bit of a problem. BifurcationKit simply doesn't solve/support initialization systems.

[TorkelE]

From a Catalyst point of view I think full support for initialization laws are not needed, however, we have the conservation laws which we need to support for this (as they remove singular Jacobian they are essential in this specific case). Previously this used to work fine though? I.e. we didn't really needed to do any initialization, and I could just manually add the solved for conservation laws as observables and use the default values stored in the conservation law parameters. However, with the latest updates this stopped working. Still not possible to not have manually defined observables overwritten by mtkcopile?

[AayushSabharwal]

I think I can make manually defined observables work. It seems necessary given the MTKBase split - users should be able to provide extra information.

[ChrisRackauckas]

Like steady state, it may need to initialize but only for initial branch selection, but in the bifurcation case you need to find all branches anyways, so the branch selection ends up trivialized here