Police letter for €30 shoplifting arrived 6 MONTHS later.

Hi everyone, I’m an international student studying in Saxony. I am truly lost right now and could use some legal advice. This is my very first time dealing with anything like this.
The Incident (November 26, 2025):
Six months ago, I was stopped by a security guard at Kaufland with €29.29 worth of unpaid groceries in my bag. I am being accused of theft (Ladendiebstahl), but it was a genuine, stress-induced mistake.
On that day, my father was undergoing a major, life-threatening surgery back in my home country. I was going through a severe depressive episode, extreme stress, and what felt like total memory loss/dissociation. I was panicked about my dad and rushing to get to my university work shift. I put the items in my bag on autopilot and walked past the checkout.
When the guard stopped me, I immediately offered to pay and tried to explain my mental state. I don’t know if he called police to the store or not. guard tried to make me sign a paper (probably a confession or house ban), but I kept explaining him my situation and if i cannot sign it because I was frantically trying to explain my situation and told him I urgently needed to leave for my shift. He kept me there for about an hour, and then eventually just let me go.
The 6-Month Gap & The Letter:
I heard absolutely nothing for 6 months. Now, I just received the police letter ("Schriftliche Äußerung im Strafverfahren"). The deadline to reply was May 20, 2026.
I missed the deadline because I am not currently living at my registered apartment—I sublet it to a friend. My friend checked the mail late and only sent me a photo of the letter today.
What I have done today to fix it:
1 Emailed the police caseworker my mandatory details (Pflichtangaben) immediately to cover the missed deadline.
2 Formally stated I am using my right to remain silent and crossed out the admission of guilt on the form because i honestly don’t know how to answer those questions in the form.
3 Left the voluntary financial section/income completely blank as well
4 Emailed my university’s legal counseling (studentenwerk) for an emergency appointment this Tuesday. I don’t know how will i get in touch with them as well.
I am incredibly stressed out. I have a few questions:
No Police at the Scene / Refused to Sign: Does the fact that the police never showed up, and that I refused to sign the Kaufland guard's paper, change anything?
The 6-Month Delay: Is it normal for a supermarket to just file a report later and have the police contact me half a year later?
Lack of Intent (Vorsatz): Since theft requires intent, how do I prove I was having a mental health crisis/dissociating over my father's surgery? Will the prosecutor actually consider this?
The Subletting / Missed Deadline: Will the police accept my email today, or did missing the May 20th deadline already ruin my chances of getting this dropped (§ 153a)?

How much could be the charges?

Visa Impact: What is the worst-case scenario for my residence permit over this €30 mistake?
Any advice from people familiar with the German system would be a lifesaver. Thank you