The strangler pattern needs a seam to strangle

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

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

location / {
    proxy_pass http://legacy;
}

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

Session sharing is the practical blocker and it is usually solvable — 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 is more expensive to run than either endpoint.