I was wondering whether the wishlist could be modified from the web
version of the Play Store while using e.g. a PC.
So far it is not possible, we must wait for the new web version of the Play Store.
Also, would the wishlist sync to all Android devices connected to the
same Google account, or is it just local to the device it has been set
Yes, Wish list is hold in Google cloud and it is synced among all your devices connected to the same Google account.
I am very happy with this feature and I use it extensively. I can even automatically monitor any future updates of apps on my wish list with a help of a new feature "Observed apps" in Changelog Droid application (CD). How to do it:
CD cannot synchronize with your wishlist because Google Play Store does not have an API so third party apps cannot interact with it. However, you can populate Observed apps in CD manually from within the CD itself or by opening Google Play on your device and sharing wishlist items one by one to CD. It seems to be tedious if you have your wishlist very long, but you will rewarded. Here is real example how Observed apps in Changelog Droid helped me:
In my country we have independent consumer organization dTest. They published in Google Play its own app dTest some time ago. But it worked only on phones, not on tablets. Because I don't want to have this app on my phone, but on my tablet, I put this app in my Wish list and shared it to Changelog Droid's Observed apps. After some time Changelog Droid informed me about new dTest version with tablet support so I was able to install it on my Nexus 7 the first day when this new version for tablets appeared in Google Play :)