I think I have the solution now, at least it has worked for me since following them on July 2nd. These instructions were given to me by an Apple Senior tech advisor, after 2 previous "fixes" didn't stick.
It appears the iPhone's Safari browser is/was making the choices as to which bookmarks (an subsequently which folders) topped my most used ones, and thus moved those to be found more quickly. Then that order of folders and bookmarks was synced to my other devices through iCloud. Did the decision makers at Apple think that we all want(ed) them to reorder themselves automatically, or is this just a bug that happens when we have 500 or more bookmarks? I was told it was the 500 mark that triggered it. I suppose the reordering works for some people, but not necessarily for everyone, not for me, that's for sure. I have been purging some bookmarks lately, especially old ones I don't use anymore, or are no longer working pages or websites, as time allows and I remember to. However, I've no idea if it will make a difference, as I've no intention of counting how many bookmarks I have anytime soon, but doing some housekeeping with them is necessary, from time to time, so it might. I'm not letting it bother anymore, now that I've fixed the issue.
On my 3rd call about this in two days, I asked to be sent to a Senior tech advisor, since the level one techies didn't know how to fix it. The Senior advisor said did. So, on to why you are here...
- Clear the history in Safari on your iPhone 13Pro. (I had already done it, so I didn't include them here, but if you don't know how, you should look it up, according to your iPhone model, before moving on).
- Turn off Safari in iCloud on your iPhone. To do this, go to settings on your phone. Tap on your name, then tap on iCloud in the list below. Scroll down to Safari and turn it off. You won't lose any bookmarks, and you can still use Safari, but no new bookmarks or folders will be added at this point from your other devices.
- Now, reset the bookmarks and folders the way you want them on one of your computers. If you only have one computer, that's fine, these steps will still work. (I have a late 2014 Mac mini and a 2018 MacBook Air, but not an Apple watch...yet).
- Check to see that the folders and bookmarks are synced correctly on your other device(s) (I reset them on my Mac mini, which synced them on my MacBook Air correctly over iCloud).
- Next, you'll reboot your iPhone. This depends on the model you have, so it might be different for others, but for you (meaning me), turn off your iPhone by holding the down volume button on the left side and the on/off button on the right side at the same time until you see a slider bar to turn it off on the screen. Slide it to Off. Wait 10 minutes, then turn on your iPhone with just the On/Off button on the right side.
- Once the iPhone is done rebooting, log into it, and follow the instructions under #2 to turn Safari back on in iCloud. This will let the bookmarks and folder re-sync to how you set them on your computer. It might take a little time, but it should be done in a few minutes.
- Check to see that the folders and bookmarks in Safari on your iPhone are ordered correctly, when you open Safari there. If they are, then turn off Safari again in iCloud on your iPhone, using the same method you did before in #2. This will prevent the iPhone from reordering the bookmarks and folders over iCloud again, and messing them up on your other iCloud synced devices, when you use Safari on you iPhone. However, no new bookmarks or folders you add or reorder on your other devices will be available, or shown in that order, on your iPhone, unless you turn Safari back on in iCloud on your phone to sync them again. Just be sure to turn off Safari again in iCloud on your iPhone, after you sync it, to prevent the phone from causing the issue again.
This worked for me. Safari has remained been turned off on my iPhone, yet I'm still able to use it and see all my folders and bookmarks in the order I want them, without any realigning going on.