Currently there is a push for hunters to switch to all copper bullets. The bullet technology has gotten good enough that solid copper bullets can be designed in a way to consistently petal and create big wound channels. They're obviously more expensive so I stick with lead for the range and practice.
At the learn to hunt deer class I went to they reviewed a study that showed that lead bullets fragment and shed when they hit the target. The study shot a hog cadaver (iirc), and noted that when they scanned the result they found lead up to 16" away from the impact point and that it was probably even further but their scanner was limited to scanning just that size. The class then demonstrated shooting an all copper bullet at a series of water jugs in a bullet trap to show how it petals.
All that to say, this is a current topic in the hunting community and people are switching away from lead. More and more manufacturers are making copper core bullets and they're coming down in price. If you're interested Barnes is the go to manufacturer for these right now.
Edit: Also bird shot moved away from lead a long time ago. It's not even legal to use it anymore.
Edit 2: Turns out lead bird shot isn't illegal to use, it's only outright banned for water fowl hunting. https://www.fws.gov/story/2022-04/nontoxic-shot-regulations-hunting-waterfowl-and-coots-us. You should also check your local laws, here in Wisconsin it's also banned for mourning dove hunting.
In 1991, the US Fish and Wildlife Service launched a nationwide ban on lead shot for waterfowl hunting to reduce the number of lead shot falling into waterbodies. Since the inception of dove hunting in Wisconsin in 2003, the DNR has prohibited the use of lead shot for hunting mourning doves on state-managed lands.
In my mind I just equated that with being banned all together. Who wants to study the law just to find out when they can use toxic shot?