You can easily find such open-source neural networks in NLP applications that have been published by Companies like Google. For example, in BERT models, you can see the BERT-Base has the following specifications:
BERT-Base, Multilingual Cased: 104 languages, 12-layer, 768-hidden, 12-heads, 110M parameters
You can find more data about other versions of BERT in the same link.
Another example is GPT models, like GPT-3:
All GPT-3 models use the same attention-based architecture as their GPT-2 predecessor. The smallest GPT-3 model (125M) has 12 attention layers, each with 12x 64-dimension heads. The largest GPT-3 model (175B) uses 96 attention layers, each with 96x 128-dimension heads.
Image Procssing Domain
Another useful domain for your expectation is image processing tasks such as image classification. Pretrained models such as VGG, ResNet, and Inception. These are mostly used for image classification tasks in different companies, and you can find their specification many where. For example for VGG-16, we can see the followings:
Another practical domain is Auto-Speech Recognition or ASR in short. One of the renowned models in this context is DeepSpeech(2) by Baido Research center. For example, you can find some info like the number of its parameters and its structure in this github link.
Note that one regular metric to measure the size of neural networks is "the number of parameters" of the network that is required to be learned in the training phase. Hence, you can compare the size of models even between cross domains by knowing their number of parameters (instead of going to more details about the number of hidden layers and their types). Although, sometimes the length (number of layers) and height (number of neurons in each layer) of the network are very important in the matter of performance and capability of the network.