Yeah, Internet search as a fallback, our chat history and "saved info" in the context ... there's a lot OpenAI, et. al. give you that Ollama does not.
You can get those in ollama using tools (MCP).
Had to ask ChatGPT what MCP (Model Context Protocol) referred to.
When I followed up with how to save chat information for future use in the LLM's context window, I was given a rather lengthy process involving setting up an SQL database, writing some Python tp create a "pre-prompt injection wrapper"....
That's cool and all, but wishing there was something a little more "out of the box" that did this sort of thing for the "rest of us". GPT did mention Tome, LM Studio, a few others....
Not sure if you're aware of it, but Open Web UI is a nice (looks like ChatGPT) Web client for ollama and anything else. It also seems to support MCP.
I did play with MCP and ollama a little, but that was scripted, not interactive.