Identifying templates from SMS text
I'm not sure I understand your problem very well but let's see.
First let me try to formalize the task as a ML problem:

Identifying the SMS of interest is a binary classification task. Your &quot;completeness&quot; score seems to correspond to the standard recall measure. It is usually a good idea to also look at precision, i.e. out of the SMS identified as relevant how many are truly relevant.
You don't really explain the second part of extracting information out of SMS of interest. In general this part might be some kind of sequence labelling problem (similar to Named Entity Recognition).

It's important to distinguish these two parts if you're going to use ML.
Now what you are currently doing is a rule-based system: you manually identify the patterns one by one, then the system just applies the list of patterns. rule-based systems are considered the ancestor of ML systems: as you noticed, it might be possible to automatize the part of identifying the patterns. Given that you already have labelled examples (training data), you could train a model to recognize the general patterns by itself. The main difficulty is to provide the model with the right features so that it can do the job as correctly as possible.
Note that in general it doesn't really work as a list of templates in the same way as what you do manually.
The question of identifying cases without looking at the whole corpus might be related to ''semi-supervised learning'', where a system iteratively learns to annotate unlabelled data from an small initial set of labelled data.