sSet-enriched categories are one possible model for $(\infty,1)$-categories, by the work of Bergner and others. They are probably the most important model from the point of view of getting actual examples of $(\infty,1)$-categories.

In fact, to give actual examples of $\infty$-categories in the model of quasi-categories, one uses various kind of nerves to get quasi-categories from various types of enriched categories, among which sSet-enriched are a notable example.

For the model given by quasi-categories, also called $\infty$-categories following Lurie's terminology, there are very good references which develop the common 1-categorical notions in the higher setting, for eg. Kerodon, HTT, or the book by Cisinski. I haven't found a similar treatment for sSet-enriched categories.

• The approach of Riehl and Verity (see for eg. this and this) is particularly appealing to me, but if I understand correctly their synthetic theory does not apply to the model given by sSet-enriched categories, is this correct or am I misunderstanding?
• Is there a reference which develops the basic theory for the model given by sSet-enriched categories?
• For example, what is an adjunction between $(\infty,1)$-categories presented by sSet-enriched categories? The naive guess would be that it is just a sSet-enriched adjunction? What is an equivalence?
• If the synthetic theory of Riehl and Verity does not apply to the model given by sSet-enriched categories, are we in the situation where we have a theory well developed for some models, and some important actual examples can only be given by applying some functor, e.g. the homotopy coherent nerve to get quasi-categories from sSet-enriched categories?