The error tells you that there is no arm64 bottle (a.k.a. pre-compiled binary) for sqliteodbc.
You can try to compile it yourself with:
brew install --build-from-source sqliteodbc
But you will obtain an error:
checking build system type... configure: error: /bin/sh ./config.sub -apple-darwin21.6.0 failed
Some work is needed to build sqliteodbc on arm64 macOS.
What you can do is using Rosetta2 (a dynamic binary translator from x86_64 to arm64). Install it with:
/usr/sbin/softwareupdate --install-rosetta --agree-to-license
Then you can install the x86_64 version of Homebrew with:
arch -x86_64 /bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install.sh)"
Create an alias in your .zshrc with:
echo 'alias brew86="arch -x86_64 /usr/local/homebrew/bin/brew"' >> ~/.zshrc
Note that x86_64-Homebrew and arm64-Homebrew are installed in different locations:
% brew --prefix
/opt/homebrew
% brew86 --prefix
/usr/local/homebrew
You can install the x86_64 version of sqliteodbc with:
brew86 install sqliteodbc
You have now a x86_64 installation of sqliteodbc:
% brew86 info sqliteodbc
==> sqliteodbc: stable 0.9998 (bottled)
ODBC driver for SQLite
https://ch-werner.homepage.t-online.de/sqliteodbc/
/usr/local/homebrew/Cellar/sqliteodbc/0.9998 (24 files, 704.2KB) *
You can check that it's really x86_64 with the file utility:
% file /usr/local/homebrew/Cellar/sqliteodbc/0.9998/lib/libsqlite3odbc-0.9998.dylib
/usr/local/homebrew/Cellar/sqliteodbc/0.9998/lib/libsqlite3odbc-0.9998.dylib: Mach-O 64-bit dynamically linked shared library x86_64
Beware of the influence of environment variables: HOMEBREW_PREFIX, HOMEBREW_CELLAR, HOMEBREW_REPOSITORY, PATH, MANPATH, and INFOPATH. You can export the right values with eval "$(brew shellenv)" or eval "$(brew86 shellenv)".