Would a Russian specialist degree (diploma in dentistry) qualify me a for a master's program in Europe? I have a specialist degree (specialist diploma in dentistry) from a Russian institution. Would I be eligible for a European (e.g., German) master's program in economics? If so, how do I use the Bologna framework to convert my degree into its European counterpart?
Different MSc programs have different requirements. Most MSc programs in Economic admit students with BSc (or equivalent degree) in Economics, or similar topic, such as Finance, Business, Mathematics, sometimes Management, etc.  Your Dentistry degree does not  fall in this category - it is not similar enough to what you want to study. Some MSc programs (called conversion degrees) will admit students with less relevant experience, but they are often run at less desirable Universities.
In principle, a specialist degree can be recognised as BSc or MSc depending on the international prestige of your University and the requirements of each particular University. There is no general rule on how a specialist degree must be converted into Bologna system degrees. However, in your case, this is less important, because as mentioned above, your Dentistry background is rather irrelevant to the Economy which you want to study.
UPD: In addition, this year many Universities in Europe prepare for a downfall in number of both local and international applications due to Covid19. It means that many programs will have to be more sympathetic to candidates with &quot;borderline&quot; profiles.  Many MSc programs are still open for applications and are more likely to issue offers this year, even to candidates who normally would not be admitted.