The SM will see it. An email gets sent to them when one is submitted. Not sure if it tells who sent it. I sent one in on my SM's day off and didn't send a text. Next time we worked together they asked about it. Could have been because I was the only shift or it had my name on it.
If you have to log on to submit it (it's been awhile since I've done one and can't remember), then it will likely say who it was from.

it's about the asm, but tbh I'm not even sure if it's something worth an incident report? and they're leaving soon anyway so does it really matter...

If it’s something against the SM call Ethics and Compliance if you are worried about retaliation

Incident reports go directly to your SM, DM and sometimes ASM. They only know who it came from if you put your name in the reporting partner slot I believe.

Depending on the store manager its typically better to document Incident with reports as they allow Managers to act on issues with more weight than just a barista/supervisor’s words.