Nginx as a reverse proxy in a subdirectory?

Question

Nginx

I want something strange, namely: to organize centralized access to the zoo from servers with web applications and make access like: example.com/webapp1, example.com/webapp2.
It seemed that Nginx would perfectly cope with the Wishlist, but no, there was a nuance: most of the applications work fine only if you hang them on the root location.
Digging in mana and Google suggested a few ideas, but a fully working version did not work out.
Comparatively working version:

set $webapp1 "http://10.10.1.13";
        location ~* /app1/(?<app>.*) {
            proxy_pass $webapp1/$app;
            proxy_redirect $webapp1/ /app/;
        }

But in some cases, applications redirect beyond their location (for example, a 302 redirect to the root). This can be fenced with crutches from locations and sub_filter, but this does not guarantee the full performance of the application.
Is it possible to solve this problem only with nginx?