The only multi-protocol repeater I'm aware of was the now-discontinued Iris v2 (I think) outlet, which was primarily Zigbee (for the outlet) but also had a (sometimes-difficult-to-pair) Z-Wave repeater inside. You might be able to find them used now, but I've also heard of some problems with older firmware revisions. Probably not an easy option anymore.
As for knowing which devices are which, I guess I've been doing this long enough that I usually know what protocol my devices, including repeaters, use, off the top of my head now (I tend to have multiples of each), but sometimes it's easy because some manufacturers only make one kind of product. For example, anything from Inovelli, Zooz, or Aeon/Aeotec is undoubtedly Z-Wave. There are a few more Zigbee manufacturers (anything Centralite made for themselves or an OEM, including many Iris devices, for example; most generations of most SmartThings devices; Ikea Tråfri and Sengled outlets, etc.). Some manufacturers make/brand both--e.g., GE has both Z-Wave and Zigbee switches (and formerly outlets), but I'd say their Z-Wave ones are more popular. If this is too much to commit to memory, I'd suggest keeping a paper or PDF copy of the manuals. You'll likely need to consult them at some point in the future to figure out how to reset or re-pair the device if/when needed, so they're good to have in some form.
But back to the mesh: given the circumstances, you have two choices: either build out both meshes, or stick to one protocol. (This is overly simplifying things a bit: Z-Wave networks with everything in range of the hub won't technically need repeaters, though if you have locks it's a good idea regardless; small-ish Zigbee networks with everything in range of the hub also don't technically need repeaters...but it's probably a good idea to with either in any case.) There are lots of in-wall options for Z-Wave, as you've discovered. There seem to be far fewer for Zigbee (the GE switch is the only one I'm aware of now; I can't find any Zigbee in-wall receptacle at the moment but know GE used to have one). There are a variety of "wall wart"-style smart outlets for each protocol. If you can hide them somewhere where no one is likely to unplug them--or can find one you don't think is ugly--they're a good option.
Personally, that's what most of my repeaters for both protocols are.
For something a little more versatile, there are some USB-powered options. This might let you hide them in better locations, and the Zigbee options at least tend to be a bit smaller here. The Dome and Aeon repeaters are repeater-only devices (no smart outlet) but can plugged in directly to an outlet (and screwed in to make removal harder) or powered via USB (so you might be able to hide them somewhere else). The Ikea Trådfri USB repeater is pretty small and, of course, USB-powered so perhaps equally easy to hide. You can also DIY it and make an Xbee 3 (or S2C) chip into a repeater with some effort (there's another thread on that here), or seek out the homemade "environment sensor" device a member on this forum also makes from time to time.
I'm not sure what kinds of devices you're talking about here.