What should we add?

This issue is based on a discussion with @Cryoris and @ShellyGarion. Experimentally, transpiling a MultiplierGate into Clifford+T produces a really high $T$ count. Qiskit has two synthesis methods for MultiplierGate: MultiplierSynthesisR17 which uses QFT and cannot be Clifford+T friendly, and MultiplierSynthesisH18 which uses controlled-half-adders and should be (but is not) Clifford+T friendly. It would be nice for the default synthesis for the multiplier gate to run MultiplierSynthesisH18 when transpiling into Clifford+T, and to adjust MultiplierSynthesisH18 to provide Clifford+T friendly synthesis when required (and in particular to understand why this currently does not happen).