Extracting data from human-to-human chat

I have a problem to solve and was hoping you could advise/point me in the right direction.

The problem is: people returning products from my niche store talk to employees via a built-in chat. They provide product details, such as brand, product ID, color, etc. Eventually employees type that data into an internal return form and push it out to processing. I was wondering if it would be possible to automate this - the manual copy-pasting/typing is pretty error prone. Thing is, the chat data is pretty unstructured - 2 humans talking, saying hi, how are you, what's the problem with the purchase, nice weather we're having, using various words for the same thing (my merch, my purchase, my order, my stuff - the thing they bought), etc.

My first idea was some kind of learning algorithm - I have a bunch of these chats, and a bunch of corresponding filled out return forms, so feels like a neural network approach could work - chat as input, forms as a goal for learning. The more I look into this though, the more problems show up with this idea - how to encode these chats in a meaningful way, how much data would I need for training, what kind of network. I spent a bunch of time and found solutions like extractive summarization which kind of do that, but almost always applicable to articles, speech transcripts, etc. All sorts of BERT and BERT-derivative models, but none used for human-to-human chat data extraction.

My question - is it possible to do this, consistently and with reasonable accuracy? And if so, is there a tried-and-tested, off-the-shelf way of doing this? Appreciate any advice on this.