docs: update Homebrew installation manual

Author: alexandear

docs/src/docs/welcome/install.mdx

@@ -78,10 +78,10 @@ Golangci-lint is available inside the majority of the package managers.
 
 ### macOS
 
-#### Brew
+#### Homebrew
 
-Note: brew can use a non-expected version of Go to build the binary,
-so we recommend either using our binaries or be sure of the version of Go used to build.
+Note: Homebrew can use an unexpected version of Go to build the binary,
+so we recommend either using our binaries or ensuring the version of Go used to build.
 
 You can install a binary release on macOS using [brew](https://brew.sh/):
 
@@ -90,7 +90,8 @@ brew install golangci-lint
 brew upgrade golangci-lint
 ```
 
-Note: Previously we used a [Homebrew tap](https://github.com/golangci/homebrew-tap). We recommend using official formula instead of the tap, but sometimes the most recent release
+Note: Previously, we used a [Homebrew tap](https://github.com/golangci/homebrew-tap).
+We recommend using the [official formula](https://formulae.brew.sh/formula/golangci-lint) instead of the tap, but sometimes the most recent release
 isn't immediately available via Homebrew core due to manual updates that need to occur from Homebrew core maintainers. In this case, the tap formula, which is updated automatically,
 can be used to install the latest version of `golangci-lint`: