Unfortunately, Instagram (like its parent Facebook) no longer allows desktop apps to upload photos. The LR/Instagram plugin hasn't worked for over a year -- it's Download section says, "Service Note: Instagram has updated their protocol and currently plugin does not work."
[Use the blue reply button under the first post to ensure replies sort properly.]
I publish by exporting photos from Lightroom Classic and then uploading them to Instagram using a Microsoft Windows application known as Blue Stacks. This runs an Android operating system within Windows, so Instagram launches in the Android operating system, and can upload directly from the Windows PC.
With the Photographers subscription you have Classic and the five cloud versions. You can 'sync' from LR Classic to LR CC (aka mobile). With LR on your phone, it is a quick step to 'share' it to Instagram. On my Android phone there is an Instagram logo with a lable of "Feed" below it. It works very well.
Would it be better for Instagram to allow direct sharing from Classic? Sure. But, the sync features work so well now, this may be good enough!