What are some possible uses for this feat?
It's so you have enough time to use the items you create or to hand them out to those that will. say you're a 9th level alchemist and you Quick Alchemy, making 2 tools or elixirs. Now you're down 1 action and have one in each hand. Unless the alchemist themselves is drinking both that means you're unless you're right next to allies, you can't get rid of both before they go bad unless an ally comes over to you to get it, burning up their actions to get to you and to drink/use it.
Now if you have enduring alchemy, you have 2 rounds to use them: you can make them, move over to an ally and give one a drink and then next round drink it yourself or move and give it to someone else.
Would allowing the enduring alchemy feat to include "bombs" be broken at all?
It's pointless most times as anyone throwing bombs will usually take Quick Bomber, meaning that when they get Double Brew, they make 2 items and if one is a bomb, they then throw a bomb all in a single action. This means they still have 2 actions left to throw the other bomb meaning it's rarely an issue using your bombs in the normal time.
The only time I can see this being useful with bombs is with Demolitionist's Set Explosives activity, which requires you to have bombs in hand already. If you had to Quick Alchemy those bombs, you don't have enough actions to get away from the explosion since you have to detonate it before the Quick Alchemy bombs cease working.
OTOH if they last until the end of your next turn, you can set it up on this turn, the next turn back away and detonate it. Normally you do this activity with Advanced Alchemy bombs (or stand in the blast radius, but Demolitionist can at least also give you some resistance to it).
IMO this wouldn't cause issues. The typical bomb use case is with Quick Bomber and it gets very little out of Enduring Alchemy even with this change.
One of the main reasons the possible use-cases for Enduring has dropped to near-0 is due to remastered Combine Elixir having no extra VV cost, when the old version did burn +1 i.reagent for the privilege.
In the old paradigm, Enduring + Double Brewing 2 elixirs was a slower, but more i.reagent efficient option versus making a Combine w/ 2 elixirs inside.
.
Old Quick Bomber didn't compress Quick Alchemy, and Double-Brewing (one) bomb + one not-bomb was the #1 use-case where Enduring provided real value, in my opinion.
1A for _____, 1A to Double Brew, 1A for the bomb throw, then next turn you could use the elixir/tool without paying the Q:Alch action tax.
(Note that the Alchemical Chart item which extends all Q:Alch durations +1 turn takes up a hand, making it incompatible with the 2-for-1A benefit of Double Brew)
The other main use-case for Enduring is simply when you only have 1A for alchemy per turn, not 2A. Enduring allows you to "clip" your Quick Alch item use between 2 turns. Note that unlike Double Brew, there is 0 action efficiency gain; you are still spending a 1A Q:Alch tax for every 1A Activate. This kinda sucks donkey balls, and is most useful to a caster or Kin who has committed hard to using 2A chunks.
The issue is that a Lab Assistant familiar is simply waaay better at this task. Once online, it just has 1A available per turn to spend on "your" Q:Alch action on your behalf. The familiar 3-ability-combo needing 2 feats while Enduring is a single feat does leave Enduring with a "real" use-case though.
(to be fair, the 4 ability familiar may be waaay better, but it also adds an entire element of risk due to AoE damage, etc. A PC who doesn't want to deal with a shoulder-monkey shouldn't get so screwed by Q:Alch action tax.)
.
Imo, Enduring should have been deleted to make room for a new feat. Or it should have been actually, ya know, remastered to fit the new Alch paradigm.
Something like allowing one Quick Alch item to remain potent indefinitely until used, but prevents that VV from recharging.