Could I be rejected at google based on this?

Sorry for the long detailed post but it drives me a bit crazy. I had a google phone screen interview for early career. The technical part of the interview itself i would say went decent. I started by asking at least around 3 claryfing questions about the problem space which i know were meaningfull based on the answers, provided a sliding window approach to the problem (it was i would say LC medium level) , discussed if they think the approach is optimal (confirmed) , provided firstly wrong time complexity but when asked again corrected myself (confirmed to be right the second time) . When coding i made a couple syntax mistakes (think: missing colon) but always corrected them , went through the first part until it was right , than got another case of the problem to calculate and did that too. At the end i asked if it was all that was prepared and i was told yes. All that i didnt do in time : 1. fix function return type to return both values needed instead of one 2. maybe forgot to force-break a loop in case last number in array2 wasnt bigger than last in array1. "Maybe" because i was asked about this part, but after not seeing it first the interviewer said something like actually it works alright in this case and we just went further. Now to the point: at the start the interviewer was introducing themselves, and the autistic stressed af moron that i am i stopped them and (kindly but still) asked them if somethings wrong because i though we had technical, (and i read that technicals usually start with the problem pretty much right away), so they said its just short intro at the start. Than i went ok, introduced myself and we went to coding. Now i'm thinking, is it possible that i just made myself look like a self centered asshole who didnt care about their intro and went introducing themselves afterwards, so they graded me harsher (at feedback i was told it was negative and not a clutch pass/fail and i got 1 year cool down period). Or, am i just overthinking it and probably missed something there in the loop and got failed for that, and the interviewer just said that it actually works fine because they decided that i should have noticed myself when prompted but i didnt? I wouldnt be asking if it wasnt straight fail feedback but since it was, and i think i got the problem right at the end , it makes me think maybe my dumb ass behavior at the start fucked me up. Thanks for reading all this if you did. I'd also like to ask: is 1 year cool down a hard rule, and do i have to wait full 1 year before asking same recruiter about the possible retaking/sending my cv aswell? Or would say 10 months work? How often do you get to retake if you havent shown significant improvement in your CV?