AI Client: expose build folder (#34118)

* add build scripts to composer

* include ./build  in the mirror

* address `exports`, `main`, and `types` props

* changelog

* Update projects/js-packages/ai-client/composer.json

Co-authored-by: Brad Jorsch <[email protected]>

* fix composer building scripts

* remove duplicated composer scripts

* add composer watch script

* move main index file to src/

* declare TS window global vars

* introduce clean script

* put compiled files in the build/ folder

* ignore build/ folder

* generate TS def in building process

* add @types/react dep

* def HOC with ReactElement type

* fix types for the AIControl component

* fix types in the data-flow lib

* fix types in Storybook stories

* update packages deps

* add connectionStatus to JPConnectionInitialState

* Update projects/js-packages/ai-client/changelog/update-ai-client-expose-compiles-files

Co-authored-by: Brad Jorsch <[email protected]>

* Update projects/js-packages/ai-client/changelog/update-ai-client-expose-compiles-files

Co-authored-by: Brad Jorsch <[email protected]>

* bump new pkg version

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Co-authored-by: Brad Jorsch <[email protected]>

Committed via a GitHub action: https://github.com/Automattic/jetpack/actions/runs/6882686924