Back to the original problem. Yesterday I thought that requestSubmit() is the right answer. However, as it was pointed out by @walterdavis, it’s not supported by Safari.
So I tried to manually fire the submit event:
this.element.closest("form").dispatchEvent(new CustomEvent("submit", { bubbles: true }))
This works in Safari and Chrome, but not in Firefox which just submits the form without Turbo 
.
So if anyone is using the custom event approach, then I would suggest to test it in Firefox.
In the meantime, I’m going to look for a solution which work in all mainstream browsers :).