Size? Do you just want visual interest, or need shade, or want it to serve an additional purpose? The Pistacia chinensis isn't evergreen.

Arbutus 'Marina', Acacia riceana or stenophylla, Parkinsonia 'Desert Museum'. You could also do one of the fruitless olive cultivars, esp one with no pollen like 'Swan Hill'. If you were willing to go a different route, a conifer cultivar.

Thanks, I like the acacia! And, the Arbutus has been on my list, just wary of the possible droppings. Anyone have experience with an Arbutus 'Marina'?

A wide-spreading tree that provides shade would be ideal. 30-50 ft high

The arbutus will drop spent parts at times other than autumn. As do pretty much all broad-leaved evergreen trees. That said you might want to consider Quercus hypoleucoides. Rapid growing unless a stunted specimen is purchased, never heavy and dumpy looking. Was on the independent garden center market in later years up here, maybe there was a representation of this same (or another distribution) down there also - with some of this material still being present.

One of these I bought and planted here from a 5 gallon pot maybe 3 years ago is now about 10 ft. tall.

Regarding the shallow roots all trees except certain desert species root mostly near the surface. Where underplanting can be a problem with particular kinds is if they produce dense mats of roots and dense, shady canopies that exclude light and rain - look next door at the redwood for an example. The redwood is also an example of how conifers generally are not suited for underplanting, at least until big and old enough for some specifically adapted kinds to be able to survive. Old as in high branching, like in a forest grove of adequate vintage.

In addition to the arbutus, I'd also consider an olive. Unlikely to develop the size you prefer but an attractive and often sculptural addition to a garden setting. And it will provide shade to the patio.

Personally, I think something that will grow to 30-50' to be oversized for that location anyway.

Yes: to begin with the installation of the planter established a scale that the ash was not in proportion with. If a replacement tree also reaches 50' then at that point it will resemble a big monster trapped in a small enclosure as well.

The evergreen background hedge looks flat topped, as though it is being kept pruned to that level. Maybe instead of putting an evergreen tree in the planter, let the hedge grow taller and choose a small deciduous tree for the planter. Something like a crape myrtle if you want bark interest, a tendency to fork.

U. S. National Arboretum Crapemyrtles

https://www.crapemyrtle.com/uploads/2/7/8/1/27814181/usna_crapemyrtleposter.pdf

Suggesting a Crape Myrtle for California feels almost sacrilegious when so many other exotic options are available on the west coast.

Crape myrtle is beautiful but not evergreen. Also quite messy so close to the patio; it actually drops flowers, leaves and bark, each at a different time. Not the best for a patio. Ask me how I know.

I agree a fruitless olive would be a great tree for this location. Big but not too big, visually attractive color and form if multi trunked, low water use, evergreen. I planted a 24” boxed Swan Hill fruitless olive 5 years ago. It was about five feet tall, it’s now about 12 feet tall. Olives are one tree that can be planted big without worries, if you spent the money for a nice 48” boxed specimen you could have an instant replacement that would only get better with time.

Have you tried https://selectree.calpoly.edu/ ? You can select characteristics and get a list of trees with lots of information about size, water needs, roots, etc. Don't put in more than 4 or 5 characteristics at a time to get good results.

Thanks, all for your suggestions and advice!

What are your thoughts on a Palo Verde?

How messy is the Silverleaf Oak? We have a 100-year-old Coast Live Oak in our front yard that we just hate. The acorns, the caterpillars, the pollen, the leaf litter...it's just a mess. But, I do like the look of the Silverleaf...and planting a CA native would feel right.

What about a Parry Manzanita?

Or a Ray Hartman ceanothus tree form? (too small?)

I still love the Olive tree, but a comment from someone at my local nursery has me doubting this tree... "Why would you plant an olive tree so close to a magnificent redwood? Mixing California and Italy seems wrong!"

I agree with above; this is a garden, not a woodland. But if you want to go native, there are lovely dwarf cultivars of native conifers - Abies concolor and PInus ponderosa, for example. Also, plants make 'mess'. True, some are messier than others, but you are unlikely to find a living tree that doesn't drop something at some point. Another tree that you might consider is Ulmus parvifolia 'Drake'. It's deciduous but here in Sonoma County it is just now dropping its leaves and will leaf out again within a month. And it blooms in the fall, which is nice for the pollinators.