Maintenance: Refactor webserver `projects` service api


1. why if this is an api method is the `request` still there? it should be the app instead, there is no concept of request in an api. or is there?
2. the search query, where does it come from? in api/specs/web-server/_projects_crud.py I did not see it

_Originally posted by @sanderegg in https://github.com/ITISFoundation/osparc-simcore/pull/6579#discussion_r1814791772_
            