I think the answer is really "it depends."

Let's look at just your body, because you are one of the many parts of nature that recycles dead organisms. You reuse some of the amino acids you eat, but you also burn a lot of them for energy. Even if you eat 100 g of protein every day, you don't put on 100 g of new muscle every day. So every day, you are burning at least some protein for energy -- turning it into basics like carbon dioxide and water and something nitrogenous. (In humans, the nitrogenous product is mostly urea.)

Also, most proteins in your body don't stick around forever. They are broken down and rebuilt. But the time frame can vary a lot. Collagen, for example, can have a very long half-life: over 100 years in cartilage and 15 years in skin according to [1]. At the other end of the spectrum, some enzymes have a half-life of hours [2]. So some of the amino acids currently in your proteins will be burned today and replaced by dietary protein. But because of the variability, it's very hard to say how long the average amino acid in your body stays an amino acid.

Similar things can be said for basically any biomolecule. For example, a nucleotide can "live" for a long time if it happens to be part of the DNA of a neuron or other long-lived cell, and for a much shorter time if it's in in the DNA of an erythroblast (red blood cell precursor) whose nucleus will soon be ejected and metabolized.

[1] Verzijl et al., "Effect of Collagen Turnover on the Accumulation of Advanced Glycation End Products," https://www.sciencedirect.com/science/article/pii/S0021925819558288

[2] Mathieson et al., "Systematic analysis of protein turnover in primary cells," https://www.nature.com/articles/s41467-018-03106-1