If you have global view/transfer enabled with HSBC accounts in other countries, they might share information if requested by authorities as stated in the legal fineprint but it should be fine if you don't activate this option.
Idk about HSBC Armenia but I have had a good experience with this bank as a retail client in 4+ juridictions (self serve, I am a very low touch client as I do everything myself). They don't bother me much, besides the sporadic CRS certification letter. Also I am Premier everywhere so there are literally no fees for almost everything I do.