Unfortunately the feature of merging images together is not supported in the Timelapse module of EO Browser.
If you really need to make a time-lapse with merged images, you could use a more manual approach but it will be more work. By setting a time-span rather than a single date, you can return merged products.
You can then download the images in EO Browser and create a timelapse using a tool locally (e.g. imagemagick).
Have you found a solution that works well for you yet? I’m really keen to find a straightforward tool that can help me compile my time-lapse without too much hassle.
I did smth similar for my school project and used this free movie maker. It made the whole process a lot easier. It had all the features I needed to sequence my images perfectly and blend them into a cohesive time-lapse.