While technology can and should be used to develop intuition, it does not help much when trying to map intuition to formalism. And that is where the epsilon-delta definition is hard to grasp; continuous is always more subtle/difficult to understand than discrete. This has already been well studied/discussed in mathematics education;

Some thoughts about epsilon and delta (this is a pretty good AMS article on the subtleties involved) - https://blogs.ams.org/matheducation/2019/08/19/some-thoughts...

Teaching limits of sequences before limits of functions in Calculus? - https://matheducators.stackexchange.com/questions/3952/teach...

Advantages of the sequence definition of limits - https://mathoverflow.net/questions/105920/advantages-of-the-...