Nothing will make the kitchen "modern"

Get 4 inch Baltic Tile to make a riser splash to the pass thru. And call it a day until you are ready to change the kitchen. If you want to paint cabinets a soft white? Perhaps.... a lot of DIY work, and expensive to be done by a pro.

I'd start a piggy bank for the kitchen I REALLY want.

It would be helpful to see the look you are trying to achieve - what you consider modern?

Agree with Jan - just get a 4" coordinating splash until you are ready to replace all the granite.

It appears you already have stainless appliances. As for the cabinets, they have a lot of detail in the panels that will look less than modern even painted. I can see they need some restaining in some areas. There are cabinet restoration companies and products out there that can restore your cabinets to looking nice until you can replace or reface them. I do think they complement the existing granite better than white would. If you insist on painting - I would replace the decorative legs on either side of the sink cabinet with more plain moulding.

In the meantime I would look up countertop styling ideas. You can bring in some potted plants, breadboards and framed pictures to lighten up the look.

Oh, I was in the same situation when we bought our house in 2014. I look for mini fixes but in the end the rest of our place needed so much mechanical and other work (all new windows, electrical upgrade, some plumbing, roof, etc) that we updated some hardware, painted, and saved. We were ready to start the major remodel when COVID hit so it took almost 2 years longer to start (with 2 rooms full of cabinets to the ceiling). I fully agree with @JAN MOYER, do the fix she suggested and save for the kitchen you really want. I’m SO happy that we did, pouring lots of money into interim upgrades would have been a waste and delayed my now gorgeous kitchen even more. Wishing you all the best.

If it isn't worth remodeling the kitchen and you want to improve it instead of remodeling - maybe because you're not going to live there long, Kylie M. wrote a blog about your issue (you're not the only one with this issue): https://www.kylieminteriors.ca/how-to-update-your-older-granite-countertops/ But I agree with the other commenters that if you think you will remodel in the future don't waste your money in the meantime. I bought a house with a similar kitchen three years ago (no black backsplash or travertine floors, thank goodness, but otherwise the same) and I am planning to tackle it in a couple years. So all I did was paint the walls. There are always a lot of things to do when you move. I know we have found other projects to work on in the meantime. Your kitchen looks functional, so you can work with it as is for a while.

Another agreement with @Jan Moyer and @kandrewspa.

Congrats on the condo buy! Before doing anything to your kitchen, please live there 6 months, start a Whole Home To Do list (with priorities and cost estimates). Allow 6 mo to discover if the kitchen LAYOUT works for you.

The cab fronts look very high-end and traditional - paint can’t make traditional cabs look modern - but you can modernize in other ways…replace cab fronts with full overlay or inset slab fronts with finger holes instead of visible hardware handles, tear down the entire “dated” pass thru wall, remove the colonial spindles. Unless major appliances are broken, it may be wise to spend money elsewhere for more impact, more wow for the buck

I do think you can improve the current kitchen, but I agree with others above: this kitchen will not look more “modern” with just new backsplash. If you are dead set on only redoing the backsplash I’d probably go with a simple pattern in a creamy hue from your flooring, but, in all honesty, none of these elements work well together because (IMHO) the floor and counters don’t mesh well. You will need to order lots of sample tiles and just try them out with the counters and floor….you’ll need some time and patience for that. Changing the counters would definitely have a huge impact and would make it easier to update. Good luck!

Those cabinets look like solid wood. Unless the layout isn’t working for you, I would get some estimates for painting them.

I agrée with Marylut: if the layout is OK for you, then check into replacing the doors and painting the boxes. I think you could make huge strides with that approach.