Edge insulation strips are definitely necessary. Since it will be tiled later, tile adhesive is sufficient. But you can also fill it with screed concrete or cement screed or anhydrite screed. Or the most expensive option with leveling compound. The only important thing is that screed is only used at a build-up height of 4-5 cm or more. Whether bonded with the old floor or on a separating layer does not matter. However, a polystyrene separating layer could worsen sound transmission to the substrate, which would be a good thing. So actually, there are hundreds of ways to solve the problem.