AI Agent modules: check if folder exists when starting the module

[hugodutka]

If the input folder does not exist and tmux is used, the AI Agent will silently start in the home directory. This leads to confusing behavior down the line. For example, with Claude Code, MCP would be configured only in the non-existent folder and the agent wouldn't report tasks to Coder.

We've already merged a fix for the Claude Code module: #124. It should also be applied to the other AI Agent modules.