at 7:41 am or so on May 1st 2024 started this test with debug on minimal and attached the resulting zip file to this post (dual monitor set up, bottom is main external hdmi monitor #2, top is secondary hdmi #3, (internal laptop display #1 disabled)
First tried Mozila Thunderbird on #3 shows titlebar button in windowed or maximized mode. sending window to #2 works but titlebar button only shows in windowed mode, not maximized mode. sending back to #3 from windowed mode works, and titlebar button shows in both modes again. repeat sending back to #2, same issue button only shows in windowed mode.
Then tried test with the default Windows Media Player app starting with #3. Titlebar button shows in windowed mode only, does not show in maximized mode (so is different than Thunderbird). send to #2 while in windowed mode works, same issue, the button only shows in windowed mode. send back to #3, same issue.
Stopped testing at this point, but also have the issue with SichboPVR4, but not quite sure how to describe because the app never uses a normal Windows titlebar, it is an overlay with transparent background in windowed mode, all icons dissapear after a moment except your titlebar button, which stays. not sure if that app maximize button actually maximizes the window or enters fullscreen mode, but in any case your button now is missing in that mode whereas previously it remained like in windowed mode (after the Sichbo icons disappear).

Enabling that setting resolved the issue for Thunderbird and Media Player (Thank You, I should have looked for that myself even though the help page describes it's purpose a little differently), but not SichboPVR4 (button only appears in windowed mode on either monitor). Posting a new minimal log result with a test of SichbopVR4 at 8:06am.

Well my success was short lived, after leaving for a couple hours and logging back in, the issue has returned for Thunderbird and Media Player. The only change I made after the success was moving the titlebar 10 pixels left and 5 down, then I rebooted and tested the apps and everything was still good at that point. I checked and the setting you had me enable is still enabled.