Yes. The entire context gets pushed through the neural network every time you respond.

There are some tricks that can be done to compress the context when it starts filling up the window while retaining much of the meaning. Think of it like summarizing the previous conversation so you start a new chat session while keeping most of the information but with much more context window available to use.

As you fill the context window it gets slower and slower to respond and for public services like ChatGPT you blow through your quotas really fast. You might only type in line to ask the ai another question but the pages and pages of the chat keep getting reprocessed. This is a major limitation with story telling and programming.