Discord has auto-translators that avoid all these problems.
Things like autoit can inject keystrokes, so in essence you can then cut and paste.
e.g. Chat snapshot, like you say, go to yandex, like you say, image -> translate, select and copy (Ctrl-C) translation, paste that back into game (with an autoit script). [Also means you can have stock translations, or broadcast one message in many languages quickly. e.g. Paste your order code in multiple languages expeditiously.]
Even easier is to get them to do all their chatting in Discord, where the auto-translators are present. Things like auto-translate to main language is present, individuals can set all messages to be translated into their own language (and vice versa), and prefixes, like '?ru ' can be used for the conversations / languages / communicants that fall through these cracks.