feat(util-genai): refactor and make API smaller and more user-friendly

[lmolkova]

Replaces the handler.start_llm(invocation) / handler.stop_llm(invocation) pattern with factory methods that construct and start spans in one call, and moves lifecycle ownership onto the invocation object. Existing code continues to work — LLMInvocation, stop_llm, and fail_llm are kept with @deprecated markers.

Before

inv = LLMInvocation(provider="openai", request_model="gpt-4o")
# inv is in invalid state now
handler.start_llm(inv)
try:
    inv.output_messages = [...]
    # need to carry both - handler and inv to here
    handler.stop_llm(inv)
except Exception as exc:
   # why not just pass exc ?
    handler.fail_llm(inv, Error(type=type(exc), message=str(exc)))

After

inv = handler.start_inference("openai", "gpt-4o")
# valid state right away
try:
    inv.output_messages = [...]
    # no need to pass handler here if happens in a different method
    inv.stop()
except Exception as exc:
    # much shorter
    inv.fail(exc); 
    raise

with handler.inference("openai", "gpt-4o") as inv:
    inv.output_messages = [...]

[MikeGoldsmith]

Looks good to me. I've left one small suggestion for separating invocation types file, but not blocking.

I see you have a few TODOs you'd like to probably resolve before merging too.

[lmolkova]

@MikeGoldsmith and @DylanRussell thanks for the review!

The todos are the existing ones - it's easy to a address them but I didn't want to include any new features into this pure refactoring PR.

[lmolkova]

/cc @Cirilla-zmh

[MikeGoldsmith]

Still looks good but has some conflicts that need resolving first.