The Immortal Jellyfish, and functionally the naked mole rat.
The lobster, though they die from being too large to molt.
That you can go 300km/h in an F1 car, doesn't mean you can go that fast on a bicycle, even though they're both in the genus "wheel-based vehicles for human transport". The jellyfish is a rather different animal. Trees can grow very old, but there's a reason why you didn't use those as an example: too far from human biology. That jellyfish may be at a similar distance.
The process of science is to determine what exactly these inferred limits actually are and how many can be overcome.
It would be a scientific process to find the limits, but I don't see a scientific reason to find out how to overcome them. Science' job description is oberving and explaining, not altering nature.
In some sciences like astronomy you just really don't have the the ability to.
With medicine it's really the entire point, it's science we learn to improve humanity.
Perhaps that explains why medicine is often such bad science. It's more engineering, really.
We have the ability to convert to becoming immortal. It actually happens to some of us. It sucks though. We call this cancer. Turns out the immortal cells become selfish. But you can scrape some off yourself, throw them in a petri dish, supplement growth media, and they will divide forever.
*sucks for the rest of the body. I'm sure the cancer itself is pretty "happy".
IANAB but lobsters are worth a look. They apparently do not get slower or weaker or even lose fertility as they age. And apparently Greenland Sharks might live for 300-500 years, are immune to cancers, and their DNA can repair itself. Maybe leaving the ocean was our ancestors' mistake.
Greenland sharks are interesting because they do everything slowly, including aging. Our best guess is that pregnant Greenland sharks have at least a decade-long gestation period. Which seems like an adaptation to cold and relatively barren environments?