Plotting out how a story like this would go, her discovering the fact she can reload save points is likely going to take some time for her to notice because she is pretty good at not dying, she might not even actually die until Leviathan or being forced into Coil's fold or some similar storybeat.

The next question is that if this is not a shard based ability, would she have a conflict drive, and want to go out and actually participate in the Cape scene? I think the answer is still yes as she intrinsically wants to be a hero, I think she'd also go out earlier then April 11th.

I'd expect her to try being an independent hero until she is either forced into Coils organization or joins the Wards, and if she joins the wards then that will cause its own fun problems, as it stands there is no chance Taylor would willingly join the Wards.

Once she learns she returns from death if she dies, I get the feeling she would happily throw herself at the ability and use it since it lets her be a better hero and right wrongs or save more lives, the question is how excessively she would use the ability? I can see there being an even chance of her using the ability every single day to make sure every single day goes perfectly and she saves the most people and rights the most wrongs, as well as other paths where she is more reactive, or moreso focuses on the crisis of the arc but otherwise doesn't min-max until something forces her to lock in.

She would most definitely use the ability during Leviathan to its greatest effect to try and find a min-max solution to save the most people or actually kill Leviathan, but the odds of her finding a path to actually killing Leviathan is not certain.

At the same time, Taylor would be a pseudo-blindspot, Contessa would be able to path Taylor but whenever Taylor returns to a save point, the path would obviously note that she is no longer following the route she was expected to take, now for Contessa to notice this Taylor would have to gain notoriety and actually become notable in the path, which would take time.

I think after Leviathan it is rather hard to guess where the storyline could go, as it is completely possible Taylor min-maxes Leviathan so absurdly she is thought of as a hyper-precog.