Bug: "cannot execute binary file: Exec format error" when installing via Homebrew on Linux x86_64

Describe the bug
I attempted to install the Turnkey CLI using Homebrew on a Linux environment (ChromeOS Crostini Debian), architecture x86_64. The installation via brew install tkhq/tap/turnkey completes successfully. However, executing any turnkey command results in an Exec format error, indicating that the downloaded binary/bottle is not built for the correct architecture.

To Reproduce
Steps to reproduce the behavior:

Environment: Linux x86_64 (Debian-based).

Run: brew install tkhq/tap/turnkey

Run: turnkey generate api-key --organization --key-name test-key

See error: -bash: /home/linuxbrew/.linuxbrew/bin/turnkey: cannot execute binary file: Exec format error

Expected behavior
The CLI should execute successfully and generate the API keys.

Environment:

OS: Linux (ChromeOS Crostini / Debian)

Architecture: x86_64 (uname -m returns x86_64)

Homebrew version: 5.0.15

Additional context
Attempting to force a build from source using brew install --build-from-source tkhq/tap/turnkey seems to still fetch the pre-built bottle (build completes in 2 seconds) and continues to throw permission denied / exec format errors. It appears the formula might be pointing to the wrong architecture binary for Linux x86_64.

Start by inspecting the Homebrew formula and the Linux artifact selected by brew install tkhq/tap/turnkey; compare their architecture with uname -m and the installed binary. Done means the x86_64 Linux installation produces an executable turnkey binary that runs the reported command successfully.