Workaround for modifying coefficients in constraints in JuMP?

There’s Constraints · JuMP, the paragraph below the part of the documentation you posted. You could also think about using GitHub - tkoolen/Parametron.jl: Efficiently solving instances of a parameterized family of (possibly mixed-integer) linear/quadratic optimization problems in Julia. This has been discussed before a number of times. See e.g. Deleting containerized constraints - #13 by tkoolen for a Parametron demo.