The command is called tldr. This was hinted at in the Conflicts with section of the brew info output that you posted.
It is also shown in the output of brew list tlrc:
% brew list tlrc
/opt/homebrew/Cellar/tlrc/1.9.3/.crates.toml
/opt/homebrew/Cellar/tlrc/1.9.3/.crates2.json
/opt/homebrew/Cellar/tlrc/1.9.3/bin/tldr
/opt/homebrew/Cellar/tlrc/1.9.3/etc/bash_completion.d/tldr
/opt/homebrew/Cellar/tlrc/1.9.3/sbom.spdx.json
/opt/homebrew/Cellar/tlrc/1.9.3/share/fish/vendor_completions.d/tldr.fish
/opt/homebrew/Cellar/tlrc/1.9.3/share/man/man1/tldr.1
/opt/homebrew/Cellar/tlrc/1.9.3/share/zsh/site-functions/_tldr
Note the /opt/homebrew/Cellar/tlrc/1.9.3/bin/tldr entry. This is automatically linked to the Homebrew bin directory upon installation, and should therefore be in your path.
% type -a tldr
tldr is /opt/homebrew/bin/tldr
You should not need to install Rust to use tldr. You would only need Rust installed if you need to re-build the binary, in which case Homebrew would install it for you (it's a build dependency, not a run-time dependency).