You seem to be confusing the construction of system prompts with "training". Prompts do not change a model's weights or train them in any way. Yes they influence output, but only in the same way different questions to LLMs (user prompts) influence output. Just because it's not available in current user interfaces to use commit messages as a prompt does not mean the model wasn't trained with them. It would be a huge failure for training from version controlled source code to not include the commit messages as part of the context. As that is a natural human language description of what a particular set of changes encompasses (given quality commits, but quality is a different issue).

There are MCP Servers that give access to git repo information to any LLM supporting MCP Servers.

For example:

>The GitHub MCP Server connects AI tools directly to GitHub's platform. This gives AI agents, assistants, and chatbots the ability to read repositories and code files, manage issues and PRs, analyze code, and automate workflows. All through natural language interactions.

source: https://github.com/github/github-mcp-server

This is hair-splitting, because it's technically not a part of _system prompt_, but Claude Code can and does run `git log` even without being explicitly instructed to do so, today.