KazO, it sounds like you are much more equipped and well versed in the very critical nature of doing trigger work compared to the average shooter. You have educated yourself on the proper sear angle and sear engagement to achieve the safe consistent trigger pull you require for your Beretta SO5. You understand that proper tempering of the engagement surfaces is important to getting a smooth pull that lasts a very long time. And you had the brains to stop using it when you determined the present trigger became a hazard.
I notice you said the present sear appears to have signs of someone working on it, and that it is visibly rounded. What none of us here know is how much material has already been removed, and if it is even salvageable.
A metallurgist could fairly easily determine what alloy the sear is made of. That would cost additional money. And then you could learn the correct way to reharden and draw the temper for steel of that particular alloy. I agree that the method recommended above would likely get you in the ballpark. But it is only guessing at this point to know the type of steel used, and whether it is an oil, air, or water hardening alloy. You could possibly do a good enough job to make it last for a long time if it was a hunting gun that sees limited use. But you are apparently a high volume trap shooter, and a trigger that works well for 500 or 1000 shots before wearing out again, or fracturing, could put you right back where you are now in a very short time period. And that's all assuming that the present sear hasn't already had too much material removed to do a good job.
Considering all that, and considering that Beretta SO5 parts are probably still available, it might be wise to try to find a new or good used sear, and fit that to your gun. Then carefully stoning a small amount of material of a through hardened part, if necessary, is unlikely to leave you with a sear tip that is not correctly hardened and tempered. Even a brand new part isn't a guaranteed fix. Years ago when I was in college, I bought a Colt .357 mag revolver, and the hammer notch fractured before it had 100 rounds through it. Every few shots during single action firing, the hammer would drop prematurely before the transfer bar came up, resulting in a misfire. As it was a brand new gun, my FFL sent it back to Colt and they replaced the hammer for free, and covered shipping both ways.