Technically speaking, broomstick putters are 100% legal in tournament play. This applies to professionals and amateurs. However, there is a slight catch. You are no longer allowed to ‘anchor’ broomstick putters against your chest.
It is important to recognize that the underlying goal of the USGA was to eliminate any form of ‘anchoring against a fixed’ point during a putting stroke.
Before rule 14.1-b was implemented, players were allowed to press the top of the putter handle against their chest, effectively creating an anchored pivot point. This also applied to belly putters, where players would press the top of the handle into their belly, also creating a fixed pivot point.
After the anchor ban rule was implemented on the 1st of January 2016, all forms of fixed anchoring became illegal. This quickly eliminated belly putters from the game of golf, but broomstick putters survived, because you can still use one provided you don’t anchor it against your chest.