I've read some of the threads in the section about updating the audio system in a w123 but I've no ability or desire to attempt any electrical DIY projects.

I'd like the ability to play audio from my mobile phone by aux input or Bluetooth.

Is this something that a commercial establishment could undertake? What would one need to have done to have this functionality and have it sound good too?

I'm sure this post demonstrates my ignorance on the subject but it is what it is.

There are auto sound etc. shops that will do this for you, depending on your location. Some of the after market radios that fit are pretty sophisticated.
Before you let them go ahead though, I would make sure they either have experience with your car model or truly understand how to remove the center
console covers and radio. If they don't they can break the tabs holding the
console cover in place or mess other things up. There are videos that show how to do this. Just search remove Mercedes 123 console.
I would also ask if they solder wires or just use heat shrink sleeves.

Becker AutoSound LLC - Mercedes BMW Ferrari Porsche Auto Audio Repairs shows some replacement radios that are available from them. The shops usually have their own sources as well.
Hope this helps.

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85 300TD

88 560SL

05 SL65 AMG

It does, thanks! Is soldering preferable to heat shrinking?

It is my understanding that heat shrinking is quick and easy compared to soldering. Soldering is more permanent and corrosion is less likely.
They will both work. The shop that fixed the mess made by another installer
uses solder.

__________________
85 300TD

88 560SL

05 SL65 AMG