The same problem just cropped up for me in the past day or two.  I didn't try closing and reopening Tiles v2.0.  I've been running Start11 and Tiles since I started running Win11 in 2021 and, IIRC, this is the first time the problem has seriously reared its ugly head.

Curiously, I've found running Groupy2 makes program windows only fill the part of the screen not occupied by the Tiles bar.  Usually, I have Groupy shut down as I find some of its behaviors annoying, so perhaps I'll have to learn to live with running Groupy2 24/7.

Without Groupy2 or opening and closing Tiles, it does seem like I can get program windows to just fill the part of the screen I want by laboriously resizing each app when it opens to not overlap the Tiles bar and Windows remembers that sizing the next time the program is launched.  Much easier to just run Groupy2 since I have a license.

Tiles seems to be Stardock's orphan child, alas.

I should also qualify my experience in the following way and check out how reproducible it is the next time I have an overlap problem.

First of all, I am typically running Dragon Naturally Speaking v15.61.  It still works surprisingly well in Win11 23H2 but doesn't always play happily with Stardock software.

Today, I did something unusual: I tried to launch Dragon when I logged onto my Windows desktop before Start11v2 and Tiles2 fully launched.  That caused a big hiccup with the Start11 Taskbar and possibly with Tiles2.  But the only problem I encountered after that was the Tiles2 bar hiding the right half of program windows, which wanted to occupy the full monitor screen.  Unfortunately, I didn't manage to put 2 + 2 together at the point I noticed the Tiles2 bar overlap problem.

Later, when I tried to launch Groupy2, which I had probably disabled as a Startup application, I got a message (which hung on the screen and couldn't be gotten rid of until I rebooted) that I couldn't run Groupy2 because I'd chosen customized Windows performance settings that have turned off almost all Windows GUI enhancements including SHOW WINDOW CONTENTS WHEN DRAGGING (a bit strange that Groupy requires that GUI enhancement).

So, after enabling the display of window contents when dragging to run Groupy2 and rebooting my computer to get rid of the hung Groupy2 notification, I got rid of the problem of the Tiles2 bar hiding program windows.

So, I probably mistakenly thought launching Groupy2 solved my Tiles2 problem, but I was probably only doing as the OP suggested, effectively closing and relaunching Tiles2 by my reboot, and that's what probably cured by Tiles2 bar obscuring problem.

If the Tiles2 problem crops up again in the future, I'll more carefully investigate whether running Groupy2 or not really makes any difference or if it's only relaunching Tiles2 that fixes things up.