Thanks ahead of time for your help! I've attuned pets to elements and put proficiency points in stats, but under that, there are ranks of the abilities (such as Leeching Strike Rank 1, 2, etc. for Earth element). There's a percentage bar that I figured required using the ability, but I've been using the abilities of my party pets for a bit now and they're still at 0%... what am I missing?

At the moment, ranking up is only possible in the Lost Grove, the most recent zone of content (generally lv60+). Presumably when the site is revamped it'll be more widely available. But for now, it's exclusive to the grove.

Only recieved in the lost grove, not in any fest zones or even in Sweet Blossom Orchard // Astryls Tranquility
For a more comprehensive answer, see my thread on ability expertise gain rates.