I won’t allow myself to be treated badly by others though
You haven't been treated badly, you received a polite, if blunt, email from your LA that they had received a complaint. How is that being treated badly?
I won’t take being spoken to like I’m five by a property agent who clearly believes a curtain twitcher over me, and hasn’t the intelligence to ask for my version of events before writing to me implying I’m at fault.
The LA does not say they believe the neighbour. They merely say that they have received a complaint and the neighbour has kindly asked that it cease. They are merely the messenger.
They could have asked your side and turned it into a huge discussion, but it's a car parking issue ffs, they probably have bigger issues to deal with. They could have ignored the neighbour but they will have wanted to create a paper trail in case a) you were the one causing issues and they needed to show that they had spoken to you b) there were any further issues c) the neighbour contacted the LL and they wanted to show they had the "issue" in hand.
All that was required was a response staying that the car was not yours, nor did it belong to your guests or anyone related to you, so the complaint was unfounded but you would be sure to keep the "no parking on the verge" info in mind while parking.
When I said the email was shitty, I meant the content and implication - it wasn’t particularly rude per se, but I didn’t appreciate the tone and guilty until proven innocent vibe
Again the LA will have just fired off the email quickly based on the information available.
You don't know exactly what message the LA received - they could have got a ranty expletive filled note about the "crime" or they could have received a complaint filled with bare faced lies (e.g. they stated they knew it was your car as they watched you get in/out) that meant the LA felt that they needed to make a response.
Tbf they have done nothing but state fact - they received X complaint about Y tenant and wanted to make Y tenant aware of the accusation so that they can modify their behaviour if applicable and if not they just need to respond to tell them they have received the message but it doesn't apply to them.
I rent and I have never had issues with my neighbours judging me, but I have in the past experienced issues with a NDN who was also renting and was causing issues - letting their dog shit right outside my back gate, where my DD played with her friends; playing loud music at all hours; leaving the dog to bark for hours on end in a terraced house etc.
I could have gone to the neighbour but I was concerned that someone who would engage in antisocial behaviour like I experienced wouldn't take to well to me coming round to complain, and I would be making myself a target if they wanted to retaliate. Therefore I emailed their letting agent and asked them to speak to their tenant. They were apologetic that I had had issues and assured me that they would pass on my concerns but ensure that it was anonymised and generalised so that they couldn't identify me as the complainant.