IMO the best place for a laundry is the main floor. It is where you spend your day and no need to run up and down for every load twice . Bring the laundry down do it and take it up when you are done. As for the laundry in the bathoom not ever a good choice unless you have a really tiny house.Is this the only bathroom ?

We'd be taking the space for the w/d from the existing bathroom setup as per the image. we would have it at the front right side

it's one of the 2.5 bathrooms we have in the house

Who will use the bathroom?

You'll also want to make sure to run the proper electrical for dryer and to see if the floor needs to be reinforced. Washers and dryers are heavy and can shimmy.

place the washer along a load bearing wall so you aren't in a middle of a joist. The middle of a joist will be like a trampoline. I have a w/d in my bathroom, but have a 60" vanity. But I love having it near the bedrooms. I have this bathroom set stacked set up against a load bearing wall. No issue with vibration or walking. You also have to be mindful of the dryer vent run, as there are limits and your manual will tell you. I also have my "Laundromat" (3 stacked old w/d Miele sets) in my concrete floor basement for all the other heavy soiled clothing from my husbands farm life living.