It is reasonable to assume that the GPT 5.5 on thinking mode has significantly reduced the error rate.

I am sorry to break the bubble but that is a baseless assumption, if not in marketing. GPT models have been sold as having "PhD-" or "MD-" "level intelligence" since GPT3. Anectodally, recent models have been improving in some areas but regressing in others. "Frontier models" have incredibly opaque performance and safety benchmarks, and as time goes on more and more training data is LLM-generated, less and less comes from humans, and models start breaking down.

In response to your point: I am mainly interested in probabilistic reliability - if it gives the correct answer 99.9% of the time, it is clearly superior to the vast majority of human beings

Again, nowhere near the actual accuracy of current models. It is a big jump from 85% (wrong >1/10 of the time) to 99.9% (wrong 1 in 1000 times). At best it would barely break 90%, which is still 1 in 10.

Interestingly, my question "What was India like before the British arrived?" produces consistently biased and misleading answers. Though I haven't asked it for the new model.

An LLM's knowledge, its "intelligence", is its training data, nothing more, nothing less. Its scope, or "purpose" is its context/prompt, nothing more, nothing less. That means answering the question though the lens of British colonialism, based on a corpus of mostly "white history". I bet that if you ask the same question using a timeframe (i.e. "before the 14th century") and don't use the word "British" you'll get a slightly less, but still biased answer.