I don't see any information in your linked Wikipedia article that supports a bio-inspired origin. In fact, researchers have been wondering whether an equivalent to Backprop might be found in biological brains, but Backprop is widely believed to be biologically implausible (see e.g. https://arxiv.org/pdf/1502.04156.pdf, https://www.sciencedirect.com/science/article/pii/S089360801...).

It's not surprising that the term Backprop is not mentioned in the original paper, it isn't mentioned in most neural network research, because it's simply the default method to optimize weights and additionally it's hidden away by modern autodiff frameworks, so no one actually has to give it any thought. But backprop is definitely used in transformers (see e.g. https://aclanthology.org/2020.emnlp-main.463.pdf, https://arxiv.org/pdf/2004.08249, https://proceedings.mlr.press/v202/phang23a/phang23a.pdf, https://dinkofranceschi.com/docs/bft.pdf)

https://courses.grainger.illinois.edu/ece448/sp2023/slides/l...

From another source:

Backpropagation Through Time (BPTT) is an adaptation of backpropagation used for training recurrent neural networks (RNNs), which are designed to process sequences of data and have internal memory. Because the output at a given time step might depend on inputs from previous time steps, the forward pass involves unfolding the RNN through time, which essentially converts it into a deep feedforward neural network with shared weights across the time steps. The error for each time step is computed, and then BPTT is used to calculate the gradients across the entire unfolded sequence, propagating the error not just backward through the layers but also backward through the time steps. Updates are then made to the network weights in a way that should minimize errors for all time steps. This is computationally more involved than standard backpropagation and has its own challenges such as exploding or vanishing gradients"