Replace calls to gRPC functions that have been deprecated

This MR addresses all gRPC-related deprecation warnings that are thrown by our linter job, bringing the list down to four remaining linting issues. While we already have an open MR for this topic, that one is quite old and doesn't address all deprecated gRPC function calls anymore, which is why I decided to open a new MR.

Fixes #1663 (closed) Supersedes !1724 (closed)