Probably Rosemary would do better than lavenders. Lavenders really don't like shade.

I would second that. We are also Z9 & sunset 23. We have a rosemary bush that was here when we bought the house 21 years ago. It grows well and looks beautiful without any water or attention. A couple of years ago we replaced our grass front yard with lavender and really struggle to keep it looking nice. I had thought it would be low maintenance, but it has needed a lot of attention. We have had to replace several plants after they died and others have bald patches. Even the healthy ones need a fair amount of pruning. Both plantings are in full sun, so I can't help with the shade issue.

We had a big bed of rosemary on the north side of a house once. It was fine. I doubt that lavender would do at all well in shade. Rosemary is also a lot sturdier in general. Lavender needs to be replanted every few years to keep it looking good.

Neither plant is particularly shade tolerant but the rosemary will be slightly more so than the lavender.

And lavender will always require at least annual (if not more frequent) pruning to keep the plant dense and well formed and delay splaying or falling open. Rosemaries require minimal pruning. Rosemary is also a much longer lived plant than lavender, often growing for decades. It is difficult to find a lavender over about 5-7 years that still looks good.......usually by them they are just a gnarly, woody mess.