I am building a custom theme and I want to make it updatable. The theme is made for my purposes only so it would not be present on the official repository and might be used for multiple clients.

Also, I would like avoiding using git for this purpose if possible.

I am thinking of maybe, if possible, having some private repository which stores the theme and every time there is an update of the theme within that repository all my Wordpress websites would ask me if I want to update the theme.

Is there any process of doing it? How to do it?