How could I have my home exterior better match the doors?

You could attempt a limewash. A company called Romabio has a line of varying shades that you can purchase and DIY or contract it out. It's also removable for the first few days if you decide you don't like the look.

You could have that stone painted or limewashed.

https://www.true-design-house.com/blog/2016/9/28/stunning-paint-colors-that-will-make-your-brick-exterior-beautiful

https://www.acepaintsfurniture.com/which-paint-colors-can-accent-red-brick

It would be easier to update the color of your trim, front door and garage door. But that's just what I would do.

I agree that changing the paint of the trim and garage door would be easier and less worrisome regarding the outcome unless you absolutely love whitewashed brick. Eventually the whitewash will need to be touched up as it's outdoors unless you do an actual lime wash.

"Real whitewash made with lime doesn't have to be recoated. It can last 70, or more, years and still look good. Thinned paint will fail in a few years."

I would consider colors such as white or a very light cream for the soffits, etc. You can see just from how the key stone pops above the garage how great white looks on the house.

Perhaps a dark taupe matching some of the bricks for the garage door or (gorgeous!!!) paint it with a faux wood finish! Your front door gives you an opportunity for a big POP of color such as a green, bright yellow

You are right the brick is not the same color or style. I would change that area to hardieplank siding in a color matching the stone. Yes definitely change that trim color, garage door and front door. You have to look at the house every time you drive up make it what you love.

If you are going to stay in this home long-term, it might be worth it to have the stone on the upper part removed and replaced with siding. Then have it painted a color that ties in with your brick. I would also paint the garage doors a color that is in the mid-range of your brick. It will make it much less prominent.

I like the stone as it is. I would paint the garage door a dark brown. This would blend and tie everything more together. And it's only paint.

Here is a site to check out. Just upload your photo and play around with paint colors

https://www.visualizecolor.com/glidden?j=41663543&e=burbank30@att.net&l=5149748_HTML&u=574777240&mid=10977649&jb=106#/

In the photo looks like dark gray or charcoal. A shade lighter would look better.

Yep. That color looks better. Ties everything together.

I would pick one of the colors of the brick (stone) that you really like and paint the front door and garage door that color

I feel if it was lighter it would blend better and the door would not be the 1st thing your eye goes to

I agree the doors don't go with the stone. Imo it would be much easier to change the doors. Why would you want to turn something that's no maintenance (stone) into a maintenance item. From what shows on my monitor the stone is shades of brown and tan and the doors are gray. I would pick a dark brown or a tan from the stone to paint the doors to make them blend in. If you want a contrast a warm medium dark green or maybe a teal. No cool colors.

Also consider that the doors are closer to the ground. Easier to get to and a lot less work to change. You could change the whole look of your house anytime you want to just by changing their color