Sugar traditionally is an essential part of sweetener syrup, the reason being that pre-dissolving the sucrose as an aqueous solution makes it much easier to mix into fluids where solid sucrose doesn't as easily dissolve - ie. cold beverages, whipped egg whites and cream, etc. The added flavourings are the optional component.
For food safety, the free water in solution is bound to the sucrose molecules. More sucrose per mass of water means less available water for pathogen metabolism (see chart below for ratios) - a 'water activity' value of 0.92 is generally recognized as inhibiting C. botulinum, and 0.85 for shelf stability where pathogens and most spoilage yeasts and moulds will not grow. These values are for just the effect of water activity, as added acid will also provide inhibitory effects.
Diabetic-friendly sweeteners would not have the same effect on water activity as their usage masses are much lower due to their sweetening powers being significantly, often magnitudes, greater than sucrose - very little sweetener is used with most of the bulk as solubilising aids and anti-caking agents.
Steeping the aromatics in just water alone will yield the equivalent of making a tea with those ingredients.
For mint, lemon leaf, and basil specifically, the aroma compounds are more soluble in an oil or alcohol-based carrier and are usually sold as such. The issue for your scenario would be resolubilizing the compounds in water-based beverages. Some manufacturers will have water-soluble formulations, ie. Amoretti's basil extract: https://amoretti.com/products/basil-extract-ws
Water Activity of Sucrose and NaCl Solutions. From: https://ucfoodsafety.ucdavis.edu/sites/g/files/dgvnsk7366/files/inline-files/133655.pdf