Walking on the pavements in Edinburgh

I moved to Edinburgh in the summer, I really could just be getting bothered over nothing but as someone who has grown up in rural Scotland my whole life, I find the fact that people walk on the wrong side of the pavement (or what I believe to be the wrong side) genuinely jarring.

I walk on the left side of the pavement and at first, I thought maybe it was just tourists being confused, as I understand that most other countries use the right side of the road, totally understandable. However, as I've become more aware of it, I notice that seem-to-be locals also walk on the right.

So my question is, am I walking on the wrong side? Is it an unspoken Edinburgh 'rule' to walk on the right?

I understand this is a very unserious situation, but I also just find it baffling that big groups have reluctance to make space for other pedestrians, sometimes it's as if I am invisible! Please take this with some lightheartedness too, I understand there is much more to be frustrated about!

Another point, of course making sure the elderly, children and disabled walkers are safe is the most important and I would always move for them! I don't mean to come across as 'expecting' anyone to adhere to rules or anything. Just a query because I have places to be and believe we could be much more efficient lol.

Edit: understand this is Reddit but just want to clarify for the people taking this more seriously than intended - I am not expecting some revolutionary change, people are also able to walk where they want, my day will go on and in no way am I trying to enforce a 'rule', maybe a different choice of word would have been more appropriate. Although many haven't heard of walking on the left, I assure you it is quite a common thing, intentional or not. Appreciate all the discussion and tips, glad to know I've not been doing something wrong and it's just a free-for-all all on the pavements. Happy walking!