The OP has been answered but I thought I’d mention a couple of technical points.
You can make bullets out of practically anything. The Soviet Union allegedly used “bullets” made from wadded paper from the pages of Pravda for point blank, back-of-the-head executions. The original KTW high penetration pistol bullet (the infamous “cop killer”) was made from tungsten alloy for density and hardness, but was later switched to steel with no drop in performance. The French THV hollow bullet had an overall low density and a very high muzzle velocity. The restricted-penetration glaser bullet is similarly low density.
For handguns, density isn’t that much of an issue as the lighter weight, lower density bullets (copper or steel) simply emerge from the muzzle faster. They don’t retain velocity so well over distance, but this is no problem over the sorts of ranges you can expect to hit anything with a handgun. Penetration on impact may be reduced which could be a problem with the smaller calibres. Another matter is polygonal rifling. A conventionally rifled pistol barrel is a cylindrical tube with spiral grooves for gripping the bullet jacket and spinning the bullet. With polygonal rifling, the barrel has a polygonal cross-section with a twist, and re-shapes the whole bullet somewhat as it passes down it. Pistols with polygonal rifling can’t fire non-deformable bullets such as the KTW and I don’t know how well they’d cope with copper or steel.
If there ever were a ban on lead bullets, I’d expect to see annealed steel bullets as the main replacement for pistol ammo, simply on grounds of cheapness. Some kind of coating might be needed to stop them going rusty though.
Rifle bullets are a whole different matter. The lower density alternatives will lose velocity with distance faster than lead, which will restrict range, reduce long-distance accuracy and reduce the terminal effect of the projectiles. Tungsten OTOH would allow a greater bullet density than lead. Hunting rounds are often softpoint to allow expansion on impact, which may be a difficult characteristic to design into tungsten bullets. Tungsten has a very high melting point which means it is not normally melted to shape it (or even to smelt it from ore). Instead it is extracted and processed as a powder and sintered into monolithic lumps. Not easy or cheap to make anything remotely complex from it!
Military rifle bullets famously have to be fully jacketed or otherwise “non expanding” so military rifle and ammo combinations tend to aim at producing marginal bullet stability. The bullet spin is only just enough to stop the projectile flipping end-over-end in the air. (In the old Lee Enfield .303 rifles this was achieved by using an aluminium tip to the bullets, to push the centre of gravity of the bullet rearwards.) This means that the bullets tend to somersault in the target when they hit, and a bullet travelling sideways does more to a person than a bullet travelling point first. Some bullets such as the 5.56 NATO reliably fragment after turning sideways at high velocity. A tungsten alternative might lose this tendency to fragment, and with the same rifling might even punch clean through the target without somersaulting, reducing the chances of killing or seriously injuring the target considerably. A way around this might be to use tungsten powder distributed in matrix of lower-density metal to end up with the same overall weight as a lead bullet.
Eventually of course, the next generation of rifles and ammo would be designed to take advantage of the different bullet materials and you’d end up with long copper bullets, tungsten-cored steel or other alternatives, with rifling to suit.