Linux: swift not found in path when installed via homebrew

[Cyanosite]

➜  swift_test swiftly use
Swift 6.1.2 (default)
➜  swift_test swift --version
zsh: command not found: swift

.zprofile was correctly configured:

➜  swift_test cat ~/.zprofile

# Added by swiftly
. "/home/cyanosite/.local/share/swiftly/env.sh"

However, the bin_dir which is supposed to be added to the path is empty with only a symlink to swiftly in Cellar:

export SWIFTLY_BIN_DIR="/home/cyanosite/.local/share/swiftly/bin"
➜  swift_test ls -al /home/cyanosite/.local/share/swiftly/bin
total 8
drwxr-xr-x 2 cyanosite cyanosite 4096 Jun 15 01:24 .
drwxr-xr-x 4 cyanosite cyanosite 4096 Jun 15 01:24 ..
lrwxrwxrwx 1 cyanosite cyanosite   35 Jun 15 00:45 swiftly -> ../Cellar/swiftly/1.0.1/bin/swiftly