Hi @cyberlisa,
I don’t have all the answers on how the webflow slider is made behind the scenes but I suspect that this behaviour can come from the fact that it is hidden when the page load and therefore the initialisation of the slider might be broken. Which would explain as well why it start working after clicking a tab (probably some redraw of the elements inside the tabs).
2 things from here that could help you out.
1 - Could you try changing the interaction to make the modal appear. (show quickview)
Instead of using hide/show you can test the following.
a - Add an initial state moving the modal -100vh on the y axis (as it is fixed positioned it would be off screen)
b - Add an animation back to 0vh just before the opacity and set its duration to 0 second
c - Remove the hide/show interaction
(you can keep the initial state for convenience in the designer but set it to block instead of hidden)
d - Do the same step for the closing modal interaction
Let me know if it does the trick for the published site.
2 - Otherwise, I did recently a custom slider tutorial which rely only on interactions and would give you more controls on how to display the different element. The downside of it is there is no autoplay feature on it but at least you could have a way to reinitialise the slider to slide 1 when closing the modal. You could even go with a webflow slider with autoplay for the page and my custom slider for the modal to have the best of both world.
Here is the thread where you can find the tutorials and the link to my project to explore the setup:
Let me know if you get further question which I might help with.
I hope it helps.
Max