error: no library targets found in package

The error

$ cargo test -p app --lib
error: no library targets found in package `app`

Why it happens

--lib picks the package's library, src/lib.rs. A package with only src/main.rs has none, so there's nothing to pick. cargo build, cargo check and cargo test --doc fail the same way, because doc tests only run for a library.

Across a workspace it's quieter: cargo test --workspace --lib skips the packages that have no library, without a word, so their unit tests never run.

The fix

Name the binaries instead:

cargo test -p app --bins       # the unit tests in every binary
cargo test -p app --bin app    # one binary
cargo test -p app              # all of the package's tests

For a workspace with both kinds of package, cargo test --workspace --lib --bins runs the unit tests of each.