suggestions for ammo for a bedside gun that won’t over penetrate the walls.
There is none.
Despite endless debate, marketing hype and gelatin tests one truth seems constant, if it won't reliably penetrate a regular wall, it won't reliably penetrate a person, and if it won't reliably penetrate a person, it won't reliably reach vital organs inside the body.
Even birdshot is nothing to sneer at, because while the individual pellets lose energy rapidly, and don't penetrate well as individual pellets, at inside the apartment ranges it is still essentially one large mass of lead moving at over 1000fps (plus the wad) and will absolutely blow a large hole in certain materials. It won't be very penetrative after that, but if you're on the other side of that first wall, birdshot can seriously mess up your day.
Accept the fact that anything you shoot that has the power to go halfway through a person will go through an ordinary wall if you miss, and might not reach the vital spot if you don't miss.
There is no magic bullet. There is no bullet that will go just deep enough and then stop, reliably. Police agencies are hugely concerned with "overpenetration", but compared to individual defensive shootings, police shoot huge numbers of people.
Most of us go our entire lives without shooting anyone. Compared to that, even a quiet area where there have only been 3 officer involved shootings in 20 years is a huge number.
Look at the 1986 Miami shootout. The 9mm round that "failed" to stop the bad guy met every penetration requirement at the time, and absolutely would go through an ordinary wall if you didn't hit your attacker.
And yet, in a real world situation, it didn't penetrate quite far enough to shut down the attacker instantly. The bad guy was mobile for about a minute and killed 4 agents and wounded 2 others before being shot again (a few times) and finally being stopped.
Hope for the best, plan for the worst, and you're seldom disappointed.