First, if you are going to deal with these things you have to learn to say "twist steel". There are many varieties of twist steel barrels of which only a very few have a damascus pattern. (The term damascus as applied to barrels implies a certain type of pattern in the twist and has no meaning beyond that.) There were solid steel barrels with a twist steel pattern in the finish.
The first trick is to be sure the gun is in sound condition. This is harder to do with a twist steel barrel as they are sometimes subject to hidden corrosion. It requires a very carful inspection and possibly proof firing. if you have plans to shoot it you need to go into this at some depth whether it's a solid or twist steel barrel before attempting to shoot it.
Given that all is in sound condition it is simply not true that a twist steel barrel is unsafe. Most of the horror stories involve corroded barrels, improper ammo, or both. The cheaper guns are more likely to have this problem both due to less quality control in manufacture and less care over the years. Be advised that most "gunsmiths" will be utterly clueless on this subject and will simply tell you it's a wall hanger.
You must use a load the gun was intended to fire. This requirement often rules out anything you can run down to Wally World and buy. Most modern shotgun ammo runs higher pressures then the old guns were meant to take. This specifically includes so called light target loads. There are suppliers who deal in ammo for these old guns. Or you can roll your own. If it's a good gun the trouble may be worth the effort. For all the modern improvements we have today shotgun performance has not improved all that much over the old stuff. They reached the point of diminishing returns years ago and modern improvements are incremental. If it's not so good a gun to start with, hang it one the wall. I have a 20 gauge with twist steel barrels that is simply not a good enough gun to go to all this trouble for.
Note that the pressure requirements have nothing to do with whether it's a solid or twist barrel but do have a lot to do with when the gun was made and what it was intended to fire. A good sound twist steel barrel is every bit as strong as a solid barrel.
And don't forget the question of chamber length. A long shell in a short chamber does not run pressure up as much as people think but it's likely to be starting out with too much pressure to begin with. An overlong case will hurt the pattern. A good pattern will buy you more performance than the extra shot in one of the modern loads. Too much shot may not result in excessive pressure but it can result in too much recoil and damage the stock. I have a 1911 Ithica Flues in 28 gauge that will take modern load pressures but I restrict to 3/4 oz of shot as a 1 oz load runs the risk of cracking the stock.