[BUG] Integration with Lazyvim's Snack terminal does not allow the window to be resized or change width configuration

## Bug Description

I'm using Lazyvim configs in my nvim (just default configs) and I've noticed that I cannot change the ClaudeCode terminal window through our current configs. If I change it in either snacks or claudecode config, it doesn't seem to work either way.

It does work if I just use `native` as my ClaudeCode terminal but the integration is not as nice as using Snacks.

## To Reproduce

Steps to reproduce the behavior:

1. Set up ClaudeCode lua config file in lazyvim configs
2. Set `split_width_percentage` in `terminal` opts
3. Start Claude Code integration and notice the window size is unchanged

-- Note it's interesting that `split_side` does work

## Expected Behavior

The window width should change according to configs. And you should be able to resize it within nvim.

## Environment

- Neovim version: 0.11.2
- Claude Code CLI version: 1.0.51
- OS: macOS 15.6
- Plugin version: 0.2.0

Reproduce the issue with the default LazyVim configuration, the Snacks terminal integration, and terminal.split_width_percentage set. Start by tracing how the terminal options reach the Snacks window, then verify that configured width, split_side, and interactive resizing behave as expected in Neovim.

Written by the indexing model from the issue text.