First step, determine if the "old Parker" has any collector value (even damaged)
And, if it has "fluid steel" barrels or Damascus/ "twist" barrels.
Next, take it/send it to a real gunsmith for evaluation. I don't mean the friendly guy who just builds ARs and mounts scopes and fixes small things by replacing parts, they may not have the experience you need. Some will say they do, when they don't, so beware....
The issue is the left barrel is split down to about 19 inches.
This is what concerns me. The barrel is split,, why? and, how??
You say the left barrel is split, it need to be checked. Split (a crack?) split (burst?
) Split from the muzzle all the way down to 19 inches???
Barrels split for two main reasons, firing with an obstructed bore, or metal failure. A black powder twist barrel coming apart due to being fired with smokeless ammo counts as metal failure.
Which brings me back to the point of having a gunsmith check out the gun.
What if the barrel is also "bad" between where the crack ends and the breech? IF so, cutting off the cracked part doesn't make it safe to shoot!!
Last time I checked, Federal law (with some specific exceptions) required shotgun barrels to be 18" minimum, or be registered as an NFA firearm. Some states have their own laws on this matter, as well, and may be more restrictive than the Federal law.
IF your gun has "twist" barrels (which may not be really obvious) it should NOT be used with modern smokeless ammunition!!
It shouldn't be expensive to hacksaw the barrels, smooth them up with a file, fill the void between the ribs, and reinstall the front sight.
This is the work needed to return the gun to useable condition, IF there is nothing else wrong with it, BUT what you need to know, first, is would the gun be safe to use after that work was done? If not, then it's an as is wall hanger display
There may be something(s) else wrong with the gun, that you don't know about. You need a guy who knows old SxS shotguns who can evaluate all of it.
Twist barrels (Damascus) were regarded as a sign of quality in the old days, and I've heard when fluid steel (modern) barrels came out, some guns had them but were finished with a fake Damascus pattern, just to appeal to the buying public. Never personally saw one, but it is the kind of thing done back then.
Grandfather had a "stub twist" Ithaca SxS. Farmer neighbor really liked the gun, and after about a "20 years" of him trying to buy it, my Grandfather finally relented and sold it to him. He replaced it with a new Ithaca with fluid steel barrels, in 1909. In the 1940s, the farmer neighbor with his old gun had "about 4 inches" of the left barrel "unravel" when he fired it. No one was hurt, thankfully. I have my Grandfather's 1909 Ithaca, its in perfect mechanical condition, still.
You really need someone experienced to check the gun out. You may have a rare collectible variant. OR it may be a decent old gun that could be returned to service, or it may be something only fit for a wall hanger or a parts gun.
You might have to spend a bit of $ to find that out, but its not wasted money. Having the barrels chopped and finished on a gun that might be a time bomb when fired would be wasted money to me.
Good Luck!