I'd wait and see where and how badly it floods when it rains heavily and if it does drain badly.

There are some options -

You could take up odd slabs here and there and plant in the spaces where they were.

You could take up slabs in a group in the middle and plant a centre bed.

You could take up slabs round the edges and create a border.

You could have pots and planters filled with lovely things lifted up and away from the boggy bits. This would bring the plants nearer your nose, if you planted scented things, but potted plants are more dependent on you for water & food.

You could make part of the plot into a bog garden.

Sounds as if you will never be happy with this if you make do and mend! Why not take up the paving and assess the drainage, once this is resolved you can have the garden you would like?

My garden has a similar problem - nothing drains away. So short of digging way down and creating a layer of gravel and then filling it back in, conventional beds are a no no. My solution is raised beds and lots of pots.
The raised beds sit on the slabs - offcuts of carpet are stapled around the bottom of the beds to stop the soil washing out.

Welcome to Goy. How big is this area? A bog garden in the middle with raised beds around the rest of the space sounds like a good idea but it really depends on how much space you have and As Beattie says do nothing until you assess how wet the area gets. Click on the A-z at the foot of the page and then on Bog Garden Plants and see what you might grow. Click on D and Dry soil plants for more suggestions.