I can’t tell you what’s going wrong, but I can tell you that example works in my Julia 1.7.0

julia> using JuMP
julia> using GLPK
julia> model = Model(GLPK.Optimizer)
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: EMPTY_OPTIMIZER
Solver name: GLPK
julia> @variable(model, x >= 0)
x
julia> @variable(model, 0 <= y <= 3)
y
julia> @objective(model, Min, 12x + 20y)
12 x + 20 y
julia> @constraint(model, c1, 6x + 8y >= 100)
c1 : 6 x + 8 y ≥ 100.0
julia> @constraint(model, c2, 7x + 12y >= 120)
c2 : 7 x + 12 y ≥ 120.0
julia> print(model)
Min 12 x + 20 y
Subject to
c1 : 6 x + 8 y ≥ 100.0
c2 : 7 x + 12 y ≥ 120.0
x ≥ 0.0
y ≥ 0.0
y ≤ 3.0
julia> optimize!(model)
julia> @show termination_status(model)
termination_status(model) = MathOptInterface.OPTIMAL
OPTIMAL::TerminationStatusCode = 1

some other basic tests

julia> using JuMP
julia> Model()
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.
julia> using GLPK
julia> GLPK.Optimizer
GLPK.Optimizer

Beyond that, a bit more of your REPL and the error message might help

So then me question is, how to update Julia WITHOUT reinstalling all packages again (I updated them with Pkg.update()).
I did not find a easy updating way in the Internet.
Tony