@tuanphan
Yes, with the help of Weglot support. As far as i understand, they added the switcher and programmed it on their back-end. I only have partial control of it on the Weglot platform. Yet, it's fixed on the page, it doesn't move with the page when scrolling down and in mobile mode, rather then being in the menu, it's fixed on the page. The problem is that it can't be moved to: header-actions-action header-actions-action--cta.
Unfortunately, Weglot support staff couldn't help any further, so here's what i did:
I used the Weglot switcher (provided by Weglot) in desktop mode and the Squarespace switcher (the drop-down switcher provided on the Squarespace platform) in mobile mode and used a lot of CSS to customize the later.
Still it's less then ideal and i wish there was a simpler solution. Perhaps by customizing one or the other switcher for both modes or, as proposed by Weglot support, by using language hooks https://developers.weglot.com/javascript/link-hooks . I tried the language hooks option, but i couldn't program it in order to see only one language button at the time (English button on french page and vice versa).
The easiest solution, it seems, would be to replace the header button with the Weglot switcher in "header-actions-action header-actions-action--cta" Do you have a suggestion?