You don't need something as heavy and random as LLMs for this, traditional ML/stats techniques will be far more efficient and likely work completely fine given how rigid/consistent transaction descriptions are. Any flavor of Bayes classification (decomposing the descriptions to individual words/"words"; including prices, possibly bucketed or distance matched as a score modifier; and accounts) would probably work great.

You could get fancy with word2vec or something similar but I'd be unsurprised if the improvements were marginal.

I don't know how the matching currently works, it may be something approximating this if not it exactly.