If you are starting from scratch with a m43 camera, then buying EF lenses kinda defeats the whole purpose of that format.
First things first: the m43 is approximately 1/2 the image diagonal of a full-frame 35mm camera, which means lenses need to cover only 1/4 the area, and that means you can use 1/8th the glass to get the same job done. That translates to much smaller, lighter, and less expensive lenses, which is the main idea of the format.
When it comes to depth of field, the variables that go into that equation are focal length, focal distance, aperture, and circle of confusion (which is related to image size and magnification). Boiling it all down, a "standard" 50mm EF lens shooting a subject 10 feet away at f2.8 on a 35mm camera is going to give similar field of view and depth of field as a 25mm m43 lens shooting the same subject 10 feet away at f1.4 on an m43 camera.
If you then place the 50mm EF lens on your m43 camera, it behaves like a telephoto lens. It doesn't give you a shallower depth of field than a 50mm m43 lens on an m43 camera--that stays 100% the same. The reason you get shallower depth of field on a 35mm camera is not due to the lens alone, but the variety of parameters (lens, distance, aperture, circle of confusion). Putting an EF lens on your m43 camera will make it heavier, unbalanced, more expensive, and will do nothing at all to change the depth of field compared to the same focal length m43 lens.
As for your desire to "do it all" for $600, architecture really requires wide-angle lenses. Really wide. Wider than you can afford for $600. But you can do something with a 12mm lens--much more than with a 14mm (or longer). For weddings, you'll want medium wide to medium telephoto. If you are trying to stand really far away and pick up candids with a long telephoto, you are doing it wrong.
A great lens that does both 12mm and the wedding range is the Olympus 12-40 f2.8: https://www.42ndphoto.com/Product/olympus-12-40mm-f2-8-m-zuiko-ed-pro-lens-62mm-/110022
It's a little more than $600, but an incredible bargain for what it does.
As for the range beyond 40mm (which is the equivalent of approx 85mm in 35mm full frame territory), a great shallow depth of field telephoto option (which again is more than $600) is the 75mm f1.8 lens: https://www.42ndphoto.com/Product/olympus-75mm-m-zuiko-f1-8-lens/110025
An f4.0 zoom lens on a m43 camera has the depth of field of an f8 lens on 35mm cameras--pretty deep. An f2.8 lens, especially toward the longer end (40mm) will give you some separation between subject and background if you are careful.
Me? I have the f2.0 zooms (14-35 and 35-100), which cost $2,000 +/-:
That's the cost of shallow DOF and really high performance on m43. There are f2.0 zoom lenses that almost cover the 35mm format, but they weigh about 15 lbs and they cost almost $100,000:
Which is why you see very few f2.0 zooms for 35mm. Any why an f2.0 zoom on m43 is hand-holdable and much more affordable.
Bottom line: if you are going for m43 for cost and weight, don't blow it by buying EF lenses. If you already have $20,000 worth of EF glass, then maybe it makes sense to spend $600 on a speed booster so that you can repurpose some of that glass for your new camera. But it's no reason to go out and get some new.