Is there improvement within what you are experiencing?

So there are a few things going on.
.Individually they may be small changes, however, the cumulative impact of doing them at the same time maybe alot for your feet/body to buffer.

As you are breaking in new shoes there can be some disruption. As you noted there is less support in the new pair. Parts of your feet may be working more then they have worked in the past. This can cause some discomfort. If you are only wearing this pair of shoes when training wear them when you are home to help ease the transition.

Implementing the foot exercises can have different parts of your foot active and doing the work which have not been active (or active to that degree) in the past. As you are working with these exercises your feet will get stronger. They shouldn’t cause pain.

Paddleboarding upped the demands on your feet and throughout the system.
Higher demands and new demands across the amount of time you were doing it. Your foot must be active and your foot is making the corrections. Smaller doses of time can help this.
After a session spending some time addressing your feet can help.

Oly shoes for snatch and clean &jerk is fine as this is what they are designed for.

Changes in programming can place different demands on the body based on the focus of the training. Doesn’t sound like your training has changed.

Having more awareness with potential impacting factors will help as your feet get stronger and you are doing new activities.