Beyond an initial square area, you might consider adding pavers for a small patio, perhaps with moss or shade tolerant ground cover between them. Any configuration that works with your yard and respects the roots of your tree will do.

https://www.google.com/search?q=pavers+with+shade+tolerant+moss+ground+cover+between+them&client=firefox-b-1-d&source=lnms&tbm=isch&sa=X&ved=2ahUKEwjIiqXrl87rAhXDGc0KHbdFChsQ_AUoAnoECA4QBA&biw=1366&bih=654

Has this particular specimen been fruiting each year? Because if so then presumably part of the time it will be dropping them on anybody and anything beneath.

yes it’s currently fruiting

we clean it up as it drops

I like Christopher’s idea. Is this area large enough or level enough to hold a picnic table + benches or chairs? I’d do something real easy and cheap for now and try it out. You might find that it doesn’t work as well as you thought.

we clean it up as it drops

Drops on a nearly empty planting bed with nobody sitting there and getting hit on the head. Or having one of the fruits drop into their drink or fall onto their plate. And with no deck, shed or table for these bombs to hit, perhaps making a startling sound each time.

Would probably work out a lot better to erect an arbor or gazebo more conveniently located nearer the house or pool, and not as close to the neighbors. And use the planting bed for plants.

I honestly would not like sitting under a tree than dropped fruit on my head I think asome nice hostas and forget the sitting area and use the rest of your yard for entertaining.

ideas:

What material is your pool deck? Looks beautiful!

Mulch it. Add pavers (or brick or flagstone) if you want to use it as a sitting space, but I'd only do that if you're not going to do a deck. Otherwise, you'd just be tearing it all back out again when you move to the next phase.

A large proportion of impermeable paving being installed would risk damaging the trees.

Dig Doug's Designs has the right idea. small patio seating area -- just enough to not have a mud hole. Fruit doesn't drop year round and you can choose seating you can move when it is dropping.

Thank you all for your ideas and that beautiful rendering Dig Doug. Ultimately we’re likely planning to build a wood deck in the area to be able to really enjoy the space to its fullest...We have a lot of paved area already with a terrace covered in large porcelain concrete pavers and wanted more earthy vibes for this corner.
We also didn’t think mulch provided the aesthetic we are looking for and is not as inviting to sit on. This is a video of the backyard currently

Oops can’t send video will add other pics soon

We laid Spanish porcelain tiles for those asking above

If mulch doesn't provide the aesthetic you are looking for, gravel is the next best low cost earthy vibe that won't be a problem to build a deck over in the future. The maintenance is some weed pulling or killing now and again with the poison of your choice and a blower as needed. There is no need to be sitting directly on the gravel. You can get any kind chair you like. Depending on the gravel base, some wiggling of the chair for level may be required.

I think a light colored gravel in a rectangular shape, get rid of the curve under the avocado, would work best with your architecture as well.