Internet under the state program (ESPD), filtering provider proxy - what are the causes of errors?

Question

Computer networks

An underserver with an opaque proxy lives in an educational institution. Recently, a new Internet channel was uploaded under the state program, for free, but here's the problem - access through the filtering proxy of Rostelecom. We made a redirect from the institution's proxy to the Rostelecom proxy, installed certificates, basically everything works, but there are problems - Yandex periodically rolls out a captcha on suspicion of automatic requests, periodically there is a redirect to the Rostelecom "stub" with a request to install a certificate (which is already installed), some resources turn out to be either open or blocked every other time (especially for some reason, Google services suffer). Those who have encountered Rostelecom's filtering proxy - do they have problems with the proxy or do they need to adjust the proxy in the institution?