There are not enough photos of your new space to make useful comments. Perhaps you should wait until you have possession of the home and start a new post.

You probably need to paint. While you don't necessarily need to pay someone thousands of dollars to paint the whole house before you move in, if the walls are beige it's unlikely that will work with your colors. Whether you pay someone to paint or DIY, you need to take time to think about what color you want. A lot of people like to paint before they move in, but sometimes you don't end up with a color you really want then because you didn't sample different colors when everything was in place. If you have a wall color you really like where you live now you could paint a room or two that color before you move, but if the lighting is different in the new house it might not look the same.

The one room you show looks like it's painted greige instead of really beige. It's possible that a greige will work with your colors. I can't tell what color the floors are. Is the rug you show an area rug or carpet? Are you planning on redoing any of the flooring?

Thank you for your comments. Floors will stay the same so I have to work with what I have. No major reno but the floors are ceramic neutral tiles. Also is an area hug that I plan on changing evenkt

I would start by getting a huge rug in a color that is not beige . Do not start a new post but just post pics of the new space here in a comment and also any questions or commnets you might have all in this original post . I need to see your furniture for sure to even begin to answer these questions. Painting the walls will be a for sure with the new colors but wait until you can post pics of your stuff in the space

There are too many unknowns to be of much help. Suggest waiting until you move in and provide pictures of room(s). You also mentioned modern Mediterranean, which is more earthy and neutral. If that’s the direction/furniture and home suits, use your bold colors in art and cushions and create small vignettes.

We continue to guess with no real help at all Please post pics of your stuff BTW often when you move into a new place your choices change I truly believe spaces tell you what color they want to be sometimes not at all what you expected. I never had gray walls until this house cried out for gray.

You can mix yours (Italy) with a neutral backdrop, but you need the furniture and rugs to make it work. Let's see more photos of what you have. You will get lots of help here, but give us more info.

Thanks everyone for your help so far. I apologize for the lack of photos. It has been a little crazy here! Here are some pictures of the house (as was listed and with the previous owners furnishings). I would like to address the red room first. That's going to be the main guest room. The blue room is also going to be a guest room, only smaller. All bedrooms have carpet, which I plan on removing and carrying the ceramic tile throughout the whole house.
I am planning on remodeling the master bath to a more "aging in place" setup. Remove the tub and make a walk in shower.
I know it's a lot and any help/suggestions/criticism is welcome. ❤️

Red room, blue room

Kitchen/dining. I need to buy a new table but will keep the slipcover chairs and server

Living room. Keeping the oversized RH sofas, glass coffee table and ottoman. Need suggestions for two chairs (preferably stylish recliners for my husband)

Master bedroom _ keeping the oversized custom made headboard and window drapes

Red room - keeping the two nightstands and the red chair and ottoman

Blue room - keeping the blue roman shade. Probably will remove the bookcase

First impressions on the red and blue room: Keep the carpet, if it looks as good as it does in the photos. A guest bedroom won't get that much wear and tear, and it is nice not to have to step on a cold tile floor. Red walls...I think they are beautiful...looks like a very expensive paint job and the color is more raspberry than red. New window treatments in this room, for sure.

Blue room, keep going with more blues. Go lighter on the three walls in the blue of the bookshelf wall...painted furniture, keep the toile Roman shade.

Kitchen/dining...this is where you can make the lemons work. Change the two brown chairs for yellow.

Yes! Love that idea!

Bright pillows for your neutral couch.