Having a De facto time machine built into the spore drive, a spare Georgiou and two Klingons providing intel on what happened at the battle qualifies as hints towards the reset. They just have to Prisoner of Azkaban it...which they can do. Empress goes and dies in phillipas place (which is fine, because if she does, she will never have been deposed in the first place, so she’s just a splinter from an unused future.) or replaces Phillipa in the walking out of the ready room scene and opens fire. Burnham knocked out Phillipa remember?
Or they go right back, and replace Michael in environmental suit with herself and she....takes the hand of the torchbearer rather than kills him.
And she does it all, and then meets the ‘real’ ash Tyler, giving everyone their lives back. (The big themes are all about not being true to yourself because of an overlaid aspect...Vulcan conditioning on a human, Human on a Klingon, mirror on Prime, Prime on Mirror....and Alice has to wake up and realise it was all a dream.)
Now...the existence of season 2 muddies that, but I would bet that was the original arc.
It will echo the ‘lets Try this again, i’m Michael burnham’ scene in the cafeteria.
Yeah. They have the means for a TL reset now (working spore drive fully stocked, Stamets isn't sick) and good motivation for a reset if they think they can use it to avert the war entirely and stop countless casualties. Given how this series shows the multiverse to work, there's no real reason to think that the Discovery would have to cease to exist either - it could just have considered to have slid into a slightly alternate universe from where it came from.
The only solid evidence that it's not going to happen, IMHO, is the spore that fell on Tilly, and the discussion on After Trek that it will be addressed in Season 2. But as long as "our Discovery" survives (whether that means duplicates of everyone running around or shifting into another universe) they could still follow up on it.
But more broadly, the reasons to not "reboot" basically have to do with things "outside the show" rather than the internal logic from the show. From a character perspective, if you were Stamets, wouldn't you go back in time to fix everything - even ensuring that your love would still be alive?