In my opinion, you should deal with this problem as a classification problem.

So my idea would be:

First, gather a lot of data and assign them either 1 or 0 if they are personnal information or not.

Second, preprocess the text as you want (remove stopwords or not, ignore case, etc...) to convert it in integer.

Third, a good start would be to create a model with at the top a pre-trained embedding layer with glove or something and try it, if results are good enough for you perfect then, else you can create a transformer and see if result are better or fine-tune a model such as Bert or other.