NEAT and neuroevolution in general are interesting approaches. I also suggest to check techniques like DENSER [1] that can be used to evolve deep networks (by using the evolutionary part on the network structure and not on the weights).
Genetic Programming (GP), however, has not evolved to NEAT (which itself is not very recent, being published in 2002) but simply neuroevolution has become one of the topics that are part of evolutionary computation (EC). For example, one of the largest yearly conferences on evolutionary computation (GECCO) [2] was just last month with both neuroevolution and GP tracks. It is however true that the success of neural techniques had an effect on the community, some effects are the discussion of the role of EC and, for example, more space given to hybrid works (see, for example, the joint track on evolutionary machine learning [3] inside the evostar event).
Related to the original post, a place where some recent research on GP can be found are the proceedings of GECCO (GP track), EuroGP (part of evostar), PPSN (Parallel Problem Solving from Nature), and IEEE CEC (IEEE Congress on Evolutionary Computation) and journals like Genetic Programming and Evolvable Machine (GPEM), Swarm and Evolutionary Computation (SWEVO), and IEEE Transactions on Evolutionary Computation (IEEE TEVC). The list is not exhaustive, but those are some well-known venues.
For a less "daunting" starting point, some recent techniques are being added to the SRBench benchmark suite [4], with links to both the code and the paper describing the technique.
[1] Assunção, F., Lourenço, N., Machado, P., & Ribeiro, B. (2019, March). Fast denser: Efficient deep neuroevolution. In european conference on genetic programming (pp. 197-212). Cham: Springer International Publishing.
[2] https://gecco-2023.sigevo.org/HomePage
[3] https://www.evostar.org/2024/eml/
[4] https://github.com/cavalab/srbench