There’s been plenty of research on the World Health Organization and its handling of crises prior to the coronavirus pandemic, such as the SARS epidemic earlier in the 21st century, and how this was a moment when supranational institutions took on more power. Whatever the merits may have been at the time, many people have argued that the WHO acquired too many powers too quickly in that period. Clearly, that can have complex legacies later on. The same scenario could be repeated. Conversely, those institutions might become wary of taking on the powers that one might want them to take, or governments might become wary of giving them greater powers.
This can lead to an inverse effect of the under-empowerment of transnational institutions in moments where, for some people, they should have been more empowered, as in the most recent pandemic. But very often, and certainly in the EU case, one of the problematic legacies is that you see both supranational institutions and States acting in concert, taking on new powers which they don’t quickly abandon afterwards, and using those powers to remake the structure of European economies, while doing damage to political norms and the rights of individuals, associations and States.