I got a rejection for a story For context, the feedback had some areas for concrete improvement. I donated in exchange for the feedback, so nothing to be really inferred from the fact they provided personalized feedback. The feedback has some strong words of praise as well. My question, regarding the part I bolded. Are they inviting me to resubmit the piece after changes, or are they inviting me to submit a different story if I have one? Or do you think every form rejection has an invitation and I shouldn't read anything into that?
That's almost certainly an invitation to submit a new story, and that's a good thing! Many (most?) places have multiple tiers of rejection forms that they send. The lowest tier is generally just a polite no without any kind of invitation; this looks more like a higher-tier form. Still a rejection, but the invitation is likely genuine—they liked your stuff and want more of it. Spiffy-ish! If you want more information, try looking them up in the Rejection Wiki. It's one of the many useful tools in the writer's toolbox.