Ok can I ask what benefit you see from having more then 1 bard inspiration active?
When I first read your post I had it as you cast inspertion / used it/ then couldn't cast it on that person again ... Casting a bard inspertion on someone that already has it sounds like a waist
The graphic animation is still around Lae'Zel, but she did not have it anymore. Do not let that confuse you.
Lae'Zel used her bardic inspiration right before the video started (which is why her extra attack + GWM bonus attack are both ready : she killed a redcap).
Her bardic inspiration tooltip greyed out instead of disappearing (when it works properly, instead it disappear once used).
You can also see a red 'arrow' on the reaction system meaning "out of ressource" (again, when it works properly, instead it disappear from the reaction system once used).
If you watch the video, you will see that despite refreshing bardic inspiration on Lae'Zel, her tooltip remains greyed out. For color comparaison, on my bard at 0:09 it is yellow.
Also, as you can see at the end of the video, Lae'Zel does not benefit from bardic inspiration during her attack.
- Even more strange - As you can see at 0:29, once bardic inspiration was refreshed on Lae'Zel, not only [Valiant Defense] [Valiant Attack] [Valiant Damage] all disappeared from the reaction system, but the tooltip in the middle is STILL greyed out.