remove calls to shutdown in close method

[quinnmil]

Changes

• This fixes an issue (detailed in Logs fail to report after django startup #31 (comment)) where the LoggerProvider was being shutdown, resulting in the otel sdk silently ignoring calls to emit.
• We do not need to call this, as the otel sdk by default attaches an atexit handler to deal with proper shutdown on app exit. https://github.com/open-telemetry/opentelemetry-python/blob/main/opentelemetry-sdk/src/opentelemetry/sdk/_logs/_internal/__init__.py#L688
• Also puts most of the emit logic into a try/finally block to ensure that we don't get stuck in a state where handling_log is never reset. - We have not observed this happening, but it was a red herring I chased when trying to debug this issue, so worth sealing that up anyways.