I use OSQP.jl for these cases. It has some nice properties for MPC in particular, such as code generation, possibly division-free operation, warm starting etc.
You can call it through MathOptInterface which is used by both JuMP and optionally by Optimization.jl
I would also suggest the recent Clarabel.jl, which is performing very well for several MPC problems I have tried. It’s for convex problems only, like OSQP, HiGHs and COSMO.jl
Unfortunately, I had seen quite a few times HiGHS failing in QP problems of mine - I should try to report them to their developers as minimal examples when I find time.
Also, it’s worth nothing that BQPD is not free. In the commercial route there is also Gurobi and CPLEX. CPLEX in particular can also solve non-convex QPs to either global or local optimality.