Based on my understanding, my nostr publishing / following depends on my cilent.

1. My client has the list of people I follow and check / show them.

2. My client is configured to post to a specific relay and if I use another client with a different relay, some of my "follower" might miss me

For both there are ways, specially for the 2nd one. But I think there should be NIPs to "fix" this. An standard way to export/import the list of people I follow on my client.