Natives are a journey & those that plant them are appreciated by the Mother. As long as city mulch you have down is 3 or more inches away from the crown you are probably fine.
I would remove it only if:

If you have access to oak leaves - California natives love oak leaves. Shred them and use this as the mulch. Again keeping it 3 or more inches away from the crown so they can breath.
Or
Rocks. A biggish rock or 3 on the hottest side of the plant, 6 to 8 inches away from the base. This creates a moist shadow in the soil that they will send feeder roots into & draw from in the hottest part of the summer.
Good luck.

If you go look around a native area there is mulch-like material on the surface, fallen leaves and so forth. Mulch is not a problem.

The mulch from the city is just fine for those natives, just keep the crowns clear.

your selections from Theodore Payne sound LOVELY!!

when we planted our native garden here in LA we used city mulch to start, 3-4" thick, but kept the mulch away from the crown of the plant (where the plant goes into the ground) and it worked out fine. 1-2 years later we got beautiful Sycamore tree mulch from a tree trimming company and used that to supplement and replace the older mulch. And it was FREE-- tree trimmers have to pay to dump their mulched up trimmings, so they're happy to deliver to you and get it of their hands. Just make sure you work w a reputable tree trimmer so you know what you're getting (not a diseased tree or something).

Just reiterating what everyone else basically said: natives will take some times to get established (but you'll be so happy when they do). Some people like to plant fillers, like annuals, as previously said, or other short-lived plants, like Gambelia (aka Galvezia) or Acmispon, to temporarily fill it in. There's a lot more choices out there.

Really glad to see another California native gardener :)

Thanks so much everyone! Glad I didn't sweep the mulch back into the green bin. ;) Thanks for the recommendations. The folks at Theodore Payne mentioned planting wildflowers so perhaps I will clear away some spots and throw some of my Shady Mix down for a little color in the meantime.

Thanks for your help as I navigate the waters of native gardening for the first time!!

Wildflowers are good, it's true. There is a saying about the growth of natives: first year, they sleep, 2nd they creep, third year they leap. Be patient!

okay - theodore payne's shady mix planted...fingers crossed...;)