What is the coating or finish for this aluminum framed Beretta?

I would expect it is anodized. I'm certainly no Beretta expert, but that's what it looks like to me.

Worn anodizing. The hard part is finding a good anodizing operation that will guarantee their work. I would start by contacting some of the pro smiths who work on aluminum framed guns. They usually have have someone that they have vetted who won't destroy your gun. Other option is one of the modern coatings like Cerakote.

This might be an option for a re-coat. Titanium Nitride, it is a hard coating that resists wear, is applied very thin (.0002" thick), and is gold in color. In the machine cutting tool industry many cutting tools have this coating and their durability is greatly enhanced. It is way more durable than anodizing.

Ive used Gruntbull http://www.gruntbull.com/ for some of my expensive paintball markers and been very satisfied with the quality of the work.
They werent cheap but did a fantastic job.

Yup,anodizing.

Lots of old Berettas turn either brownish-yellow or greenish as they age.

I think it gives the gun character, personally.