Design responsibility is allocated via the scope (clause 21.1) and only your project manager has the power to change the scope in accordance with clause 14.3. If you wished to transfer design responsibility for a part of the works to the contractor, your project manager would have to give an instruction to change the scope under clause 14.3. Otherwise design responsibility remains with you.
Obviously if the scope is changed to state the contractor is to design a part of the works, the contractor will be responsible for designing that part of the works in compliance with the scope and the applicable law (clause 21.1 and 11.2(6)). If stated in the scope, the contractor will also have to submit its design to the project manager for acceptance in accordance with clause 21.2.
As you say, by proposing a change to the scope, the contractor is submitting a contractor’s proposal in accordance with clause 16.1. If your project manager accepts this proposal, the project manager will change the scope under clause 14.3. As part of the instruction to change the scope, the project manager could also change responsibility for the design of a part of the works to the contractor, otherwise it remains with you.
Note however that if your original scope contained illegal or impossible requirements, the project manager will have to change the scope to rectify the issue (see clause 17.2 & 14.3).