^The biotech companies are definitely expanding in Cleveland, but they tend to gravitate toward the medical centers in and around University Circle. They also don't use a whole lot of office space - that's not to say they're not part of the building boom, but they're generally not the typical tenants of downtown office towers, especially new construction. As you said, Eaton Corporation is looking to expand (bursting at the seams, actually) and according to some sources - the CEO is looking to make a "legacy" project for Cleveland. Here's hoping that doesn't translate into "corporate campus in Brecksville"
Atlantan, the Public Square tower is a joint proposal from Jacobs Group and Hines (one of the largest developer/management firms in the world). Currently it's a glassy 21-story design from Gensler. As you can imagine, some armchair critics want a "supertall or nothing" on that site but in this market and economy, a 21-story tower is much more viable. There's not a whole lot of information forthcoming, as you can imagine.
As far as the Flats East Bank, the entire site has been demo'd and they're moving into site prep. The most activity is over at West 9th and Main Avenue (just north of the Main Avenue Bridge), where a 20-story office tower is planned. I might be wrong, but it could be as much as 23-24 stories because there's a parking garage base. They have a crane set up for sheet piling which will delineate the footprint of the building. Here's the rendering from the website, which really doesn't reveal much:
After that, there's are two to three residential midrises (15-18 stories) - one of which will be incorporated with a 150-room hotel. They've signed 1 Hotel to operate that.