chore(llmobs): raise in public api methods instead of logging (#14941)

## Description

Modifies the public-facing LLM Observability APIs to raise instead of
logging where appropriate, unless they are invoked from
auto-instrumentation, in which case we still log.

## Testing

Updated the tests we have, which failed without change due to the errors
being raised instead of logged.

## Risks

Breaking change for `ddtrace==4.0.0`

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Co-authored-by: Yun Kim <35776586+Yun-Kim@users.noreply.github.com>
Co-authored-by: Emmett Butler <723615+emmettbutler@users.noreply.github.com>

Author: 3 people