I just bought this gun from GB. I am told by the seller that the guy he bought it from worked at S&W.
Congrats on your find!
Those two digits hand engraved in the barrel (& slide) are normal markings that the assemblers in the S&W Performance Center put on these finely hand fitted pistols.
All of the 3566 Limited's (I guess that's what you bought?? Need more info

) have their barrel stamped that way on the hood.
I don't know what's up with the double recoil spring setup? Either someone made their own "replacement recoil spring" (because the exact PN# for the factory recoil spring is unknown, though I've posted what will work in its place) or it was a early/later mod by the factory?
What is your SN#, minus the last two numbers if you don't want to reveal them?
You probably can still get a 9x19 barrel from Briley for a 3566 Limited. Make sure you get it fitted from them. Let me look up who you need to contact for that, if you're interested? Five years ago when I got mine they were $300.
PS: Can you measure the exact diameter of your guide rod? As far is I know the 3566's only had a single recoil spring on a .290" dia guide rod. Guide rods that were designed to work with double/nested recoil springs (like the 4013TSW etc.) had a skinnier guide rod that was .237" in dia.
The factory barrels are closely fitted but should slide out at the proper angle.
We don't know what you have exactly because to haven't shown up the whole pistol & you piggy-backed on this thread of a unknown model. S&W made several variations of 356TSW pistols. You need to post more pics & details if you want the proper answers.
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