I don't have a 32-bit machine handy to find out by trying, and I've been unable to find out from the versions of Bitcoin Core which one was the last .tar.gz version that will run on a 32-bit intel machine?
I'd usually always recommend to self-compile. It is so easy that it seems pointless downloading binaries.Code:
git clone https://github.com/bitcoin/bitcoin.git
cd bitcoin
git checkout v24.0.1
./autogen.sh
./configure
make -j $(nproc)
sudo make install
cd bitcoin
git checkout v24.0.1
./autogen.sh
./configure
make -j $(nproc)
sudo make install
Note that this will also work on Windows running 32-bit MinGW in addition to 32-bit Linux. Although @nonce you forgot the very important step of building the DB4 database by running contrib/install_db4.sh.
Of course, there is already a version for ARM Mac/Linux, and 32-bit Intel on a mac was never a thing anyway, so you don't have to worry about that.
