Hey!
I don't think you are overthinking it (+ I would probably be having the exact some worries)! Personally, I would send a quick follow-up now just to clarify to the graduate recruitment team. It is very unlikely to come across as annoying at all - if anything, it shows that you are organised and keen to make sure that they have the accurate information that they need. Something like a small correction is absolutely fine, and I think they'd rather know now then later down the line when they have already made arrangements.
You could keep it really brief, perhaps something along the lines of: "Just to clarify my previous email, my prior commitment actually runs until the 13 May rather than the 12 May - apologies for the confusion. I remain very keen to attend the insight day and will prioritise being available where possible".
This way, you are being clear and organised, but still showing enthusiasm and commitment to the firm! It is probably better to flag it now rather than wait and only raise it if they suggest the 13th, as it avoids any last-minute complications and shows good communication. However, even if you left it, I don't think it'll be a big issue - try not to stress too much about it!
Best of luck with the final stage assessments, I'm sure you'll smash it!!
