all the modal pop-ups that I see after I click close or save, there is no confirmation that the action is completed. Is that necessary?
The answer is simply yes.
One basic UX rule is the visibility of system status.
Users should always be informed of system operations with easy to understand and highly visible status displayed on the screen within a reasonable amount of time.1
In the case of saving settings in a modal there are two options:
Show a confirmation message in the modal itself and leave it open. The user will have all the time needed to understand what happend and what to do next (making additional changes or closing the modal).
Save and close the modal and display a confirmation message in the form of a alert or toast or something else that is permanently and clearly visible (and audible in the case of a screen reader user). This way users get around the application a bit quicker and is often better suited for experienced users.
In the case of just closing the modal without saving. The focus should return to where it was before the modal got opened, no extra notification is needed for that. It's standard for screen readers to notify focus changes. A modal is just a section just like any other section on the page, it's just visually presented differently.