How to set up https haproxy proxying on backend with ssl certificate authentication?

Question

HAproxy

Interaction scheme:

Client (ssl certificat)-->haproxy балансировщик --> web app (аутентифицирует по ssl сертификату клиента)

several applications are "spinning" on the web app, you can get to them at the address of the form https://host_nlb_vip/app_name
for this, in haproxy I made a config of the form:

listen https 10.10.10.10:443
       mode tcp
       source 10.10.10.10
       
       server srv1 ip_srv1:20000 check
       server srv2 ip_srv2:20000 check backup

such a configuration in tcp mode successfully proxies requests with an ssl client certificate and applications work.
But I still need to "resolve" traffic like https://host_nlb_vip/special_app_name to another pair of backend servers.

Use frontend and

acl app_list path_beg -i /special_app_name
       use_backend app_backend if app_list

will not work, since you have to use the http protocol, not tcp .
How else can I pass the client's ssl certificate through the balancer in this case, without converting it?