The old method of installing Jenkins is not deprecated in favour of a Homebrew installation.

Install Homebrew as per this arcticle https://markjesson.co.uk/2020/02/27/installing-homebrew-on-macos/

Start by running:

brew install jenkins-lts

You should see output similar to the following: –

==> Downloading http://mirrors.jenkins.io/war-stable/2.204.2/jenkins.war
==> Downloading from http://mirror.serverion.com/jenkins/war-stable/2.204.2/jenk
######################################################################## 100.0%
==> jar xvf jenkins.war
==> Caveats
Note: When using launchctl the port will be 8080.

To have launchd start jenkins-lts now and restart at login:
  brew services start jenkins-lts
Or, if you don't want/need a background service you can just run:
  jenkins-lts
==> Summary
🍺  /usr/local/Cellar/jenkins-lts/2.204.2: 7 files, 63.9MB, built in 37 seconds

Start Jenkins using the following command: –

brew services start jenkins-lts

Jenkins will now be available on: http://localhost:8080. Follow the customisation prompts to complete the installation.

You can restart by running:

brew services restart jenkins-lts

Or update by running:

brew upgradejenkins-lts

Useful links:

https://jenkins.io

https://brew.sh