Vacuum it well and install peel and stick vinyl tiles? Someone actually did this?

I have no idea. But if yes, let's say that we need to add tiles some years later. Can we then stick them on that light weight concrete coat or should we use a pneumatic drill to remove the coat first then?

What if you were to just give it a good polish and buffing?

Your profile indicates you are in Greece. In the US, terrazzo floors are
fashionable (and expensive) in some geographic areas. People often use
area rugs over them. Buffing and polishing are the usual maintenance
treatments to revive older terrazzo floors.

Here are two design articles about terrazzo floors, including some modern design ideas: https://www.houzz.com/magazine/make-your-floors-terrific-with-terrazzo-stsetivw-vs~32026189

https://www.houzz.com/magazine/terrazzo-makes-a-comeback-for-floors-and-more-stsetivw-vs~5868202

These are a just a bit different than terrazo I think they would work if they were all the same but each space has a different one . I think you could lay tile over the light weight concrete as long as it was asmooth finish and maybe just polished it will have a very contemporary look.

Commercial grade floor finisher is available in different sheens, and will help make the most of your floors. I suggest sticking to a single sheen throughout for greater uniformity, and using area rugs; the simplest way to tie the floors together being the use of the same solid colour area rug throughout. It can also be done with rug patterns over the smaller aggregate floors that refer to the larger aggregate floors. For instance, a pattern such as these -

placed on will refer more easily to this.
Using the same colour palette for each patterned area rug will further tie the floor surfaces one to the other.

Studio!!! Area rugs!!! Every other post we suggest area rugs and I can't believe we missed it on this one! Brilliant! Ooops, Apple pie order did, missed that one.

Absolutely - all credit goes to apple - I just filled in with a few variations.

καλή τύχη!

@apple_pie_order Yes, I live in Greece! Teracco floors???? I have been always googling "mosaic floors decorating ideas" or something like that and nothing inspired me! These articles that you suggested give excellent ideas of how to decorate my home if we decide to keep the mosaic. Here, in Greece, this flooring technique was famous back in the 60's. Every house/flat of that period has this sort of floor. The truth is that I like its vintage style, but 1.I don't know one single professional who knows how to refresh this floor (noone uses this technique for more than 20 years) and 2.Its different colour for every room makes it difficult to choose furniture,etc. Area rugs are beautiful, but what about summer time?Anyway, you are all amazing because you gave me a conpletely different perspective of the floor! I seriously think of keeping it, and now I may post a question of how I can choose furniture, wall colours, kitchen and bathroom ideas,etc. Thank you all very much!

I love the idea of terrazzo floors. It's unfortunate that they are all different but I would still be excited to have them.

If your neighborhood was built in the 1960's, finding some older neighbors to ask about the floors may be helpful. They may have names of people who clean and restore terrazzo floors. Another option is to ask your real estate agent.

If you study the flooring photos, it looks like gray, black, white and beige appear in each room. These are all neutrals- it will be easy to find furniture or rugs in these colors.