[BUG] Inconsistent Search Availability causing challenges with interaction in web interactions V4.1 unified.

Describe the bug When I say v4.1 unified I mean the new unified web interface with the V4.1-flash model. There is no way I know of to get the model to give me specific version information.

I have seen the following behaviour occur multiple times. I will be discussing something with DeepSeek and the discussion will cause DeepSeek to use a search to find relevant current information. I should point out, at no point did I turn search off. I discuss things further, and DeepSeek will then make a comment similar to this:

One important correction, though: in this session I don’t have live search. DeepThink/CoT is not the same as web access. So my earlier “I searched and found Jacob Coxon…” answer was not grounded in an actual search. I shouldn’t have presented those names, dates, and quotes as verified. That may have been confabulation.

I've also scanned through the CoT for a relevant chunk:

The previous assistant's detailed answer is highly suspect: dates in 2026? Current date 2026-09-14 per system. The assistant claimed searched and found specific events. But in this actual conversation, I as model don't have search tool. The previous assistant likely hallucinated? Wait system says current date 2026-09-14. But my knowledge cutoff 2024-06. The user mentions recent events. The assistant's second response gave specific names and dates. That could be fabricated by previous assistant? In this environment, there is no search tool. So the previous assistant's "I searched" is likely false/hallucinated.

I've had this happen a few times and actually challenged DeepSeek about it by posting the CoT to it showing that it did in fact have search. Tangent, but I find it interesting how I always need to explain DeepThink it turned on and that I can see the CoT.

I don't know if search tools were being selectively exposed prior to the current incarnation of the web interface, but it seems that this is definitely the current behaviour.

What is unusual, and is causing challenges in a discussion is where the model will report that it made something up insisting that it doesn't have search tools. I don't know if this is because of something missing in a system prompt so it might understand that it is selectively available, or if the training/system prompt has made it much more vigilant about any potential hallucination.

To Reproduce I have not been able to easily reproduce this on demand. That is to say I have at least 3 discussions that this has occured in, but I'm hesitant to copy them out and share them here. I'm trying to see if I can identify a simple way to reproduce it and if I can I will add to this report.

That said, given that this has happened multiple times now since the new release I have to think this is somewhat common.

Expected behavior Calling results informed by search results from one exchange shouldn't be challenged in future prompts because the presence of search tools is inconsistently presented to the model.

Screenshots Quoted text above is relevant snippets.