Sounds mostly correct to me.
Low-Level Wrappers
If I remember correctly, the functions returning file descriptors in libbpf, mostly defined in tools/lib/bpf/bpf.c, have always been very low-level. This is the case for bpf_load_program() for example, which is no more than a wrapper around the bpf() system call for loading programs. Such functions are still available, but their use may be tedious for complex use cases.
bpf_prog_load()
Some more advanced functions have long been provided. bpf_prog_load(), that you mention, is one of them, but it returns an error code, not a file descriptor. It is still available as one option to load programs with the library.
bpf_object__*()
Although I don't think there are strict guidelines, I believe it is true that most example now use the bpf_object__*() function. One reason is that they provide a more consistent user experience, being organised around the manipulation of an object file to extract all the relevant bytecode and metadata, and then to load and attach the program. One other reason, I think, is that since this model has been favoured over the last releases, these functions have better support for recent eBPF features and the bpf_object__*() functions offer features that the older bpf_prog_load() workflow does not support.
Libbpf Evolves
At last, it's worth mentioning that libbpf's API is currently undergoing some review and will likely be reworked as part of a major v1.0 release. You may want to have a look at the work document linked in the announcement: Some bpf_object__ functions may be deprecated, and similarly there is currently a proposal to:
Deprecate bpf_prog_load() and bpf_prog_load_xattr() in favor of bpf_object__open_{mem, file}() and bpf_object__load() combo.
There is nothing certain yet regarding the v1.0 release, so I wouldn't worry too much about “deprecation” at the moment - I don't expect all functions to be removed just yet. But that's something you may want to consider when building your next applications.