feat: Allow LiteLLM backends to utilize filter functions #33337

Before Submitting

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• I checked whether this already exists on the dev branch or latest source.
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• This request is not a security vulnerability.

Problem

This is similar to #32672 but for LiteLLM connections. Right now we have one LiteLLM connection that is our parent org , where we get a single Bearer token for our whole org to access models like Opus 5. We rely on filter functions to handle our accounting through OTEL metrics but we've noticed if I set the Connection in Open WebUI to be Provider=LiteLLM then none of our inlet or outlet functions are called.

Desired Behavior

I'd like Anthropic passthrough with LiteLLM to still call filter functions since we need our organization's accounting and metrics to identify who in our org is using Opus 5 while LiteLLM just shows our shared hpcgpt token as the usage so our Open WebUI metrics give us details into who's using the shared resource.

Why This Matters

We don't manage the LiteLLM we're using and we have a single shared bearer token for our entire org's usage so even if we rely on LiteLLM reporting, it's all just the same user and there are limits as we don't manage the parent organization's LiteLLM. We rely on our organization's metrics to identify who in our org is using Opus 5 through the Open WebUI connection.

Examples or References

No response

Alternatives or Workarounds

For now we've set Provider=Default but seems like Provider=LiteLLM on the connection should still allow us to use filter functions.