Senesce is in quite a few dictionaries, so it's a little surprising it wasn't allowed in Chi all along. It will be from now on, along with senescing and senesced.
These words are certainly rare compared to senescence and senescent, both of which we class as common. Thus, in the News on the Web corpus, senescence appears 2520 times and senescent 1832 times, but senesce has only 57 occurrences while senesced and senescing each have even fewer appearances. So these added words will be classed as rare.
The term normally applies to a living organism, but can be used more widely, as in a 2019 article in the New Yorker: "Though neutron stars rotate more slowly as they senesce..."