bubbletea's alt screen isn't triggering when run as a bash subcommand

**Describe the bug**
I'm trying to run a bubbletea app as a bash subcommand where all the UI gets sent to an alt window that the user interacts with and when the app closes I can write some data to stdout and capture it. Basically the script would look like `output=$(./fullscreen)`. When I try this with the [fullscreen example](https://github.com/charmbracelet/bubbletea/tree/master/examples/fullscreen), it just hangs for 5 seconds without displaying the alt screen. Is this possible to do with bubbletea's implementation? I know it can be done with tcell, and I'm getting back the escape code `\E[?25l\E[?1049h\E[2J\E[1;1H\E[1;1H\E[?25l\r`.

**Setup**
Please complete the following information along with version numbers, if applicable.
- OS: windows
- Shell: bash
- Terminal Emulator: git bash

**To Reproduce**
Steps to reproduce the behavior:
1. Build the [fullscreen example](https://github.com/charmbracelet/bubbletea/tree/master/examples/fullscreen)
2. Run `$(./fullscreen)`
3. Observe that the UI isn't shown
4. Receive error after 5 seconds about escape string `\E[?25l\E[?1049h\E[2J\E[1;1H\E[1;1H\E[?25l\r`

**Source Code**
N/A

**Expected behavior**
I'd think the alternate screen would show for the 5 seconds and then the command would terminate

**Screenshots**
N/A

**Additional context**
N/A

Start with the fullscreen example linked in the issue and reproduce `$(./fullscreen)` under Windows Git Bash. Compare its behavior with the reported escape sequence and five-second timeout; done means establishing whether alternate-screen output can work in this command-substitution setup and documenting or validating the result.

Written by the indexing model from the issue text.