With all pieces in place the update from PHP 8.1.12 / 7.4.31 to 8.1.13 / 7.4.33 was very smooth. A simple change to the .env, file bumping the versions and then a make build.
For sure, the PHP installations homebrew maintained on my previous machine worked good but they came in an uncontrolled manner when doing a brew update.
Life is good!