I recently purchased a GE Enbrighten Zigbee Toggle-Style Switch and GE Enbrighten Zigbee Toggle-Style Dimmer. I quickly noticed these do not have button capabilities (push, doubletap, held, released) like their ZWave counterparts do.
Are there any HE compatible toggle-style Zigbee switches with button capability?
I'm not sure; it's possible the new-ish GE/Jasco Zigbee switches/dimmers support double taps (and similar button events) like their Z-Wave equivalents do, but I'm not sure anyone has tested or confirmed or that any built-in Hubitat driver will get you them natively.
If you don't mind waiting, Inovelli has announced the Blue Series, which is basically a Zigbee equivalent of their Red Series, including the multi-tap capabilities: ZigBee Dimmer Switch | Project New Horizon (Blue Series) - Projects & Roadmaps - Inovelli Community
According to the timeline on that page, they are expected to have certifications complete in February and a recent post suggests a release date planned for Q1 (presumably after that). If you don't want to be disappointed, I might plan for delays, but they're using a different manufacturer for Zigbee than they were for many of their well-delayed Z-Wave projects, so you might not actually be disappointed. 
Will these Inovelli Blue Series switches be Toggle-Style switches? I have yet to see any Toggle-Style Inovelli switches. They all appear to be Paddle-Style.
Ah, no, I missed the toggle-style part (though FWIW it's difficult to find these in any style, as I hinted at above)--I think they're just doing paddle/Decora-style now. Is your only concern appearance? Smart toggle switches always look different from "regular" toggle switches to me, anyway (they rest in the center, not up or down--paddle-style ones, do too, but it's far less noticeable IMHO), and it's easy to swap out a wall plate, but I understand you might be aiming for a specific look.
Yes, looking to keep the same appearance with paddle style.
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