Unfortunately, this kind of use case isn't currently supported in the way you describe. RStudio Connect expects a single manifest file for a given directory, and multiple manifest files in one directory is not a supported pattern.
What we typically recommend is that similar pieces of content (for example a Shiny app and a Plumber API) are both subdirectories of a project. Shared code / functions between pieces of content is best achieved by writing an R package. That package can then either be manually installed on the RStudio Connect server and identified as an external package, or it can be distributed via an internal repository, like RStudio Package Manager so that it is available to deployed content.
An example of this pattern can be seen here: https://github.com/sol-eng/bike_predict