The strangler pattern needs a seam that already exists

Routing some URLs to a new application and the rest to the old one is the whole technique, and it works only where a clean seam is already present.

location /api/v2/orders {
    proxy_pass http://new-service;
}

location / {
    proxy_pass http://legacy;
}

# the two questions that decide viability:
#   where does the session live, and can both read it?
#   who owns the database during the transition?

Session sharing is the practical blocker and is usually solvable with a shared store and a common cookie domain. Database ownership is the hard one, and the honest answer during a transition is that both write, temporarily, with a plan and a date. A strangler with no completion date is just two systems, and the intermediate state costs more to run than either endpoint.