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It came out that vue routing was not my problem.
I reverted the vuejs app to be only managing dynamic content and created another project to manage the landing page.
Then I was able to configure a subdomain to manage the dynamic part of the site while the main domain was dedicated to the landing page.
In the end, the routing was made at level of the DNS, using A records to drive the request to a project or the other.
Source:stackexchange.com