Vinyl flooring in the kitchen / Beam ceiling sagged / Should I lay it on tiles?

There is a screed layer under the tiles, beneath that OSB boards and below that beams.

What year was the house built? Wooden beams age and can also sag. Take a laser distance meter and measure the distance to the ceiling in the middle of the room, then stand next to it with 4-5 people. If the distance to the ceiling has increased by more than 5mm, a structural engineer should be your advisor, a kitchen is not light.

It is always exciting to read the answers!
To the questioner:
Simply laying something over the sunken area is not an option!
I would definitely first get to the bottom of the cause of the sinking.
That means: removing the grout between the sunken tiles with a oscillating saw and diamond blade, vacuuming everything thoroughly and carefully loosening the tiles with gentle hammer blows. There aren’t many of them.
Keep these well because they will be reinstalled in the same place later.
Now carefully open the area exposed by the tiles further in depth with hammer and chisel, paying attention to any special features of the substrate.
In this way, you will encounter the causative element in the floor structure and keep the extent of the damage very manageable.
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If you later want to lay PVC over the entire surface, the entire tile surface must undergo a thorough cleaning or be ground with a diamond disc.
Then prime (dispersion for non-absorbent substrates) and skim coat over the entire surface.
This prevents the grout patterns of the ceramic covering from showing through the thin PVC covering (something that looks bad).
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Good luck: KlaRa

Thank you for the tip, we lay vinyl and not PVC.