The short answer is, you want to remove anything that’s broken. That said…
It’s kind of an interesting question with many facets, but I’ll comment on the magnets. Definitely want to get a magnet out as soon as possible. The materials used are highly oxidative and crumble and fall apart when exposed to oxygen. Iron rusts and falls away whereas lead forms a patina.
When it comes to something like a chip implant, there are several factors and variables that will affect the outcome and relative safety of leaving something in. The first thing is the bioresen we use to secure the internal components inside the glass… if it covers all the critical components then there is less chance of breakdown and leaching… but this is not something I would ever want to rely on. The resin is not there do perform this function and it’s not a design goal to cover everything inside, just enough to take up most of the void air space.
I personally don’t know if the ferrite rod of the antenna would degrade over time or not. I believe there are some plasticizers involved in making those rods which might protect it from oxidation, but I have no idea and I’ve never tested long term exposure to ion rich fluids before.