Usually fig IDs also need some leaf photos, so that would help.
Have you checked out Figs 4 Fun?

http://figs4fun.com/Var_O_info.html

Carla in Sac

Thank you Carla, yes I've perused that site, its a huge database. I have no reason to believe that the variety is a rare one. I am trying to stick with popular figs, hoping its obvious to someone.

Its most likely the victim of a tag error.

Most of the leaves are 3 to 5 lobes. Pics of young leaves added below.

The figs are very ripe and so the pink has faded a bit into the yummy jelly.

I vote for not a celeste, figs are too green and too large, I do grow several celeste figs.

Looks like that bird is eating a breba, are they all on last year's wood so far? Might be English Brown Turkey.

Yes, all figs now are breba - on last year's wood. I will watch for differences (if any) with the coming main crop. My current best guess is that it's a Kadota.

I will also post better pictures of the leaves soon.

At first I thought they might be Italian Honey Figs, but the leaf is wrong. They do look delicious.

not italian honey either

Below are a few pictures of the leaves. I hope someone out there will recognize what it is...

Aside from the pale exterior color, it is dead on for English Brown Turkey. Do they ever get browner than that?

The exterior of the fruit does not get brown unless being in sun ... due to sun scorch. ... Unfortunately the camera and lighting/ background makes the exterior appear darker than reality. I will post more, and better, pictures when the main crop comes in. Thank you!

With the new posting of your leaf pictures, this very well might be Italian Honey. I think it's been far too hot for this Mediterranean native. My Fig didn't get watered while I was gone and so looks a bit disreputable, but this is what it looks like this morning:

One thing is not:Celeste

One thing it could be Kadota