I have a CC subscription, with Lightroom Classic on my desktop (Windows 10) and the Lightroom app on my phone/ iPad. It works brilliantly BUT keyword tags don't synch between the desktop and the app. Everything else does - including metadata changes such as title or copyright - but keywords entered on the desktop don't appear in the app and vice versa.
Unfortunately, syncing keywords between Classic and Lightroom for mobile and vice versa is not supported.
Lightroom for the desktop and mobile apps don't support hierarchical keywords whereas Lr Classic does. This may seem like something that can be overcome, but apparently it wasn't deemed to be a priority.
In certain conditions, keywords entered in Classic will be available in Mobile. This is accidental, and only occurs if before syncing the photos you did a Metadata > Save Metadata and those photos didn't have smart previews at that time. To deliberately send keywords to Mobile, don't sync the photos and don't generate smart previews until you have entered keywords in Classic and done a Metadata > Save Metadata. Now sync the photos and the keywords should appear in Mobile. This is a one time thing and any further keyword changes won't sync.