Boy that is a steep hill!
Your pool is right under it? Wow!
DOn't kill that grass what ever you do, til you immediately replant something else there!
You have to worry about erosion on that hill, for your pools sake.
The very best plants for erosion are grasses, (there are some gorgeous grasses youo can plant on that hill, that includes bamboo, sumac, but I think your zone may be too hot for sumac, day lillies, which are awesome and grow anywhere, no maintaneous,
I think I would look into daylillies, go to your local nursery in the spring and see what kind will do well for you where you live.
You can plant the daylilly in with the grass already there, just clear some soil, plant the daylilly and move on to the next one, the grass already there won't hurt the daylillies at all.(Since you like flowers).
Whatever you do, keep the grass there til you get a substitute or the hill will be in your pool.

A few ideas come to mind. Not sure what part of So. Cal you are in but these would be appropriate.

1. Some kind of ice plant.
2. Native CA plants (native to your area); CA poppies, lupines, etc. Ceanothus is a native shrub w/blue flowers.
3. Combination of daylillies, natives, ice plant.

You might want to go to a local nursery and see what they have to offer. What direction does your hillside face? Does it get morning or afternoon sun? That will factor into your decision on what to plant too. CA poppies can be grown easily by seed and they reseed like crazy.

Here is a link that might be useful:

Almost all those wildflower type plants are annuals and only grow part of the year. I recommend that you dig out the slope right behind the retaining wall to give it a little freeboard. That is some space for runnoff to go before it overflows into the pool. The more the better but three inches would be a good start. I have had a lot of success with vetiver grass. It is a tropical grass from India that is not invasive. It can survive on just over 15 inches of rain per year once established. It also has an extensive root system to stop erosion and the crown can get buried and the plant just moves the crown up instead of rotting. Plant that right along the wall and then plant some big shrubs behind it like manzanitas or sages. Daylilies are pretty tough plants too.

Our place had apple mint growing in lots of wrong places, but it's turned out to be great left to colonize one of our steeper slopes. Of all the crazy things growing on our mountainside, I think I'd go with apple mint over all else if I needed a ground cover for a super-steep place. It will attract bees when it blooms, though, which you might not like around your pool.

Those wildflowers at the top of the slope look like mallows of some kind, maybe Lavatera.

I like your palm tree. Looks like Trachycarpus. Very hardy and has flowers when it's taller. It also drops fronds, but not often.

What you put on your bank really depends on how much time you have to stay on top of the care needed for the first year or so until any plantings get established.

There have been some lovely suggestions offered already: the iceplant and the local Ceanothus. There are varieties that spread beautifully to smother. Otheres are taller and more bushy. They come in a small range of colours, mostly blues and purples and they can provide a succession of flowers over weeks.

I liked the idea of the California poppies. They are so tough! And there are colours other than the standard 'orange'. You might want to plant 'pools' of them among Ceanothus to give a fairly strong visual impact. A 'Pacific' colour scheme suitable for strong sunlight. Pastels tend to get a bit lost in hard light.

The iceplants can be very effective - big sheets of colour usually in 'hot' tones, although there are softer pinks available. And, for seriously tough sites - Gazania, Arctotis, Anigozanthis (kangaroo paw - which comes in a pleasant range of flower colours dark red to interesting green.) They're usually perennial.

Climbers and sprawlers - Bougainvillea, Campsis, Trachelospermum (which smells delightful). Instead of climbing a trellis they can sprawl down the bank, needing only a trimming with shears to stay civil. Bougainvillea has thorns, however. As do the carpet roses and Rosa 'Nozomi'.

That's a fairly steep slope so work across it rather than 'up/down' to reduce the risk of rain damage. Leave strips of grass to catch the run-off and protect your pool from mini-mudslides. At least until your plantings are spreading out.

Before planting ANYTHING - check with your local garden centre to see if it's safe for newbies. Some things look so innocent when you see them as a cute little cutting in a teeny pot... and then you find they have rule-the-world tendencies. English ivy would be one. Cortaderia would be another. Many South African bulbs, such as Watsonia, can happily fill acres. So can Ornithogalum. And, if it's not too hot where you are, asparagus fern and ginger plant can take over in no time.

If you should chance to like them - and don't mind some spiny-ness consider bromeliads. There are many hardy varieties that happily live outdoors, flower fairly regularly and make a good groundcover. And aren't fussy.

Ice plant! It's lush, neat, and no weed whacking required, EXCEPT you may get weeds popping up between the plants...

The house across the street from my late mother-in-law had her corner hill covered with weedy ice plant. Once that succulent takes hold, it's really slippery to walk on just to whack or pull the weeds.

There's always landscape cloth with gravel and select plants, but I think you may need to terrace.
Suzi

Bamboo is dreded by many because it has deep roots and is fast growing and takes over. It is also beautiful, can be managed with concrete structures and some of the species of bamboo clump rather then "run". Once you commit to it,you commit to a plant you can cut down and it will grow back in one season. The roots will be there. You will have to make sure that you have a subsurface structure to maintain where it will go. It will stop erosion. It is forever green. It provides shade and beauty. Pick an area and try it to see if you want your entire hill with this plant. Research varieties and some large experts and suppliers are in California. I had it in my front yard (giant bamboo) -- gorgeous. The day littlies I have (20 years worth), blocked it from entering that section of the yard and my hedge. But my roses had to be transplanted. It did not challenge mature trees. I maintained it with a deep concrete block barrier. It did run. It was hard to get out if it went towards th roses. My son had regular bamboo and he ended up with a nursery providing a poison that killed the roots. I do not know the name. He says he cannot plant anything for 3 years in that area. A tree is also there and it is unclear if it will survive the treament. If California would replant the fire ravaged areas (I used to live in Pasadena) it would never have erosion problems or mud slides again. Bamboo cannot be destroyed by fire. the roots help it grow back within one season.

I visited a friend in Ramona California yesterday, and her slope is planted with beautiful drought resistant Statice. It reseeds every year and is just a gorgeous blue purple mass of color.