[tab-bar] How to show something in the right side?

[Rodrigo Morales]

* The question

Have any of you managed to insert some content in the right side of the
tab-bar (the one that is shown when tab-bar-mode is enabled)?

For those who don't know, the current behavior of =tab-bar-mode= is to
show the name of opened tabs starting from the left side, so if you have
3 tabs opened and your font is small enough, the names will fill the bar
less than the middle of the screen. This means that there is an empty
space that could be used for something else. For this reason, I would
like to show the current time (i.e. 10:10AM) in that part of the screen
because most of the time that part is empty. Some users use "polybar"
for accomplishing this, but I was wondering whether it was possible to
do this with "tab-bar-mode" without much tinkering.

* Additional context

I could also make the time be shown in my screen with
=display-time-mode=, but I don't particularly like this because this
makes the time be shown in all modelines, so if I have 4 buffers, the
time is shown in the modeline of each buffer (i.e. 4 times). I would
rather the time be shown just once.