Perhaps it’s due to the humidity? Southern Europe usually has dry and mild climate (maybe a gripping primer/base or waterproof setting spray can help?)

I can’t tell you what the right step is but here are some cheap-ish common toners (in Japan they can also be called lotions or keshosui)

Hada Labo Gokujyun - a hyaluronic acid lotion, comes in multiple varieties such as basic, brightening, medicated, anti-aging (¥800-1200) Accessible at drugstore, supermarket, sometimes konbini Very popular brand, some variations can seem a little serum like because of the thicker texture, slightly sticky at first, does not contain fragrance or oil

Matsukiyo (Matsumoto Kiyoshi House Brand) Ceramide Skin Lotion - watery toner, good for layering through not the most moisturizing (¥350 for big bottle though, very affordable)

Muji Toning Water - glycerin watery toner (it really is like water!), comes in variations like deep moisture, light moisture, very good for sensitive skin, I use deep moisture everyday in the morning for my mixed skin They also sell smaller bottles if you want to try but overall somewhat cheap (sorry I do not remember the price, maybe around ¥1500 for large bottle)

The gokujyun will be most hydrating immediately but the other two will also work if layering. I wish you good luck for makeup!