no library targets found in package `current_project`

I am very new to emacs and are trying to set it up for rust development.
When I am in a *.rs file and M-x rust-mode this error pops up:

Suspicious state from syntax checker rust-cargo: Flycheck checker rust-cargo returned 101, but its output contained no errors: error: no library targets found in package `learn_async`

Try installing a more recent version of rust-cargo, and please open a bug report if the issue persists in the latest release.  Thanks!

I updated cargo rust with:
rustup update
and updated all my packages with paradox.
Emacs: Doom
OS: Fedora
config.el:

[...]
(after! rustic
  (setq lsp-rust-server 'rust-analyzer))

(use-package lsp-mode
  :ensure
  :commands lsp
  :custom
  ;; what to use when checking on-save. "check" is default, I prefer clippy
  (lsp-rust-analyzer-cargo-watch-command "clippy")
  (lsp-eldoc-render-all t)
  (lsp-idle-delay 0.6)
  ;; enable / disable the hints as you prefer:
  (lsp-rust-analyzer-server-display-inlay-hints t)
  (lsp-rust-analyzer-display-lifetime-elision-hints-enable "skip_trivial")
  (lsp-rust-analyzer-display-chaining-hints t)
  (lsp-rust-analyzer-display-lifetime-elision-hints-use-parameter-names nil)
  (lsp-rust-analyzer-display-closure-return-type-hints t)
  (lsp-rust-analyzer-display-parameter-hints nil)
  (lsp-rust-analyzer-display-reborrow-hints nil)
  :config
  (add-hook 'lsp-mode-hook 'lsp-ui-mode))

(use-package lsp-ui
  :ensure
  :commands lsp-ui-mode
  :custom
  (lsp-ui-peek-always-show t)
  (lsp-ui-sideline-show-hover t)
  (lsp-ui-doc-enable nil))

(rustic and lsp mode both don't work either but I am starting with rust-mode, because it told me to open a new issue)

Reproduce the rust-cargo checker error from M-x rust-mode using the reported Rust project setup and configuration, then compare the checker behavior with a package that has no library target. Inspect how rust-mode invokes rust-cargo and determine whether the binary-only package is handled correctly or requires clearer guidance; done means the reported setup no longer produces a misleading checker failure.