Isn't there a hotel that is both connected the convention center AND has free breakfast?  thanks in advance!

I don't think that there are any connected that also have a free breakfast. Now, if you don't mind going about a block out, Staybridge Suites (on S West St) had it. Embassy Suites (on W Washington St) shows that they have it as well. Fairfield Inn & Suites (on W Washington St behind the JW Marriot) says that it does also. Aside from those, you will have to start going out a few more blocks.

I think Springhill Suites might have in the past? It's been a while since I stayed there.

Some of the connected hotels have concierge lounges where free breakfast is offered. Often, you can add on access when you check in for a fee, or get access for free if you are part of the loyalty program (YMMV). We have had 'free breakfast' at the Westin for many years this way. Except for 2021, where the lounge was closed. We are hoping that it re-opens after their construction is complete!

Embassy Suites' popularity is undoubtedly due in part to its pretty excellent free breakfast buffet (and on-demand omelette chef).  I know it is only debatably connected since it is a block away, but as I understand it any hotel connected via the skywalks is technically connected!