I have tested this - the focus only seems to go temporarily to the hint, and returns to TC when the hint disappears. It looks like it has been like this for many years, so I prefer not to change it, sorry.
But a hint is not some full-fledged window on which you can actually click.
Ok, more precisely, we can click - but no action should occur! And so happens in all other windows applications.
And what - the tooltip is not drawn standard? but as a full-fledged mini-window? With its queue of messages in processing?
Maybe it's time to take another library, which is sharpened for drawing tooltips, in order to get, as another plus, the ability to draw in a more modern and more convenient way - for example, fields could be added to a tooltip implemented by another library, necessary for the output, specify the maximum width for the tooltip, after which it would wrap the output to the second/third line. Well, a more necessary plus could well be that the focus would no longer run away from the program.
But not to leave it just "as-is" because " It looks like it has been like this for many years"...
You can intercept the click of the LMB and hide/suppress the window with the hint, and then focus on the element under the cursor, thereby bypassing the problem of deactivating the TC main window.
It's complicated. Currently I set a timer on mouse down which removes the tip after a short delay. Removing it within the mous down handler was causing inexplicable crashes.