Third vote for getting a professional involved, but i'll still offer my layman's suggestion given that you're just soliciting general ideas at this point. If it was my space, I'd switch the bathroom and the laundry room around, keeping just one of the walls currently enclosing the toilet. Its hard to estimate precise measurements from the drawing, so it may not be feasible, but here's what i mean

I agree you probably need to centre the vanity and the cabinet on the wall or they could look a bit odd! You don't say why you don't want a space between the window and the vanity - just my opinion, but I would think 300mm could be quite useful for a bin, a clothes basket or box, or a small stool for putting clothes on? The only alternative to leaving a space, is to fill it with something as the response above suggested. To avoid it interfering with the window, you could make this something lower, so it sits level with the top of the vanity. This could be built in and the wall lining put over it to create a single "shelf" level with the underside of the vanity top, or if you can find some freestanding open shelving of the correct width, which could also be cut to the correct height, you could wedge that between the wall and the vanity side when fitting the vanity. Just bear in mind also, that you'll lose some of your towel hanging space if you put something too high in the space.

Depending on latches and fixing area, etc - you could get a good glazier with a bit of finesse to custom make a mirror to fit into the window area, and then just centre the vanity below the window. Provided the window glass is obscure, it will still look like a window from the outside, but you'll have an interesting recessed mirror in your bathroom! (hope that makes sense) But, If you want a seperate shower then it looks like you'll have to alter a lot of plumbing anyway, so you might as well move the vanity while you're at it.

Your client putting trust in you was the right decision! amazing transformations! Love the natural light in particular as thats a great spot for a post gym pump flex for a good selfie!