Here is just a subset of the rights guaranteed by the USSR Constitution: speech; press; religion (both to profess and refuse to profess); assembly (including a specific right to demonstrate); participation in lawmaking; inviolability of the person (from warrantless arrest) and of the home (from unlawful entry or search); privacy of all correspondence (including phone conversations); right to challenge actions of government officials and bodies in court; right to a job; work week limited to 40 hours; free medical care; welfare payments in old age, sickness, or disability; free housing; free education; academic freedom for scientists.
It's a very good list, and what I listed above isn't even half of it [1]. Precisely none of those were actually respected by the government. Having a Bill of Rights is great, but having a tradition of limited government, checks and balances, and rule of law is what gives those guarantees any weight.
[1] https://www.departments.bucknell.edu/russian/const/77cons02....