It seems that, under the common influence of French, and maybe the capitalisation from German, Russian follows the same paradigm as most if not all the Slavic languages, like Bulgarian, Macedonian, Serbo-Croatian, and Scandinavian languages, including Finnish, although they are shifting towards using it less anyway.
It is not actually clear if Russian formal вы is always letter-case, certainly for some of the other languages it is technically not the case, not for Serbo-Croatian.
Another answer mentioned German, which is essentially correct, but it is easy to form a misconception about the role of letter-case pronouns in German - that it specifies the formality, like T-V.
Consider that there is also a letter-case Du. https://www.duden.de/sprachwissen/sprachratgeber/Gross-oder-Kleinschreibung-von-duDu-und-ihrIhr explains well when it can be and should be letter-cased: for direct address.
It just happens that the informal sie is inherently never a direct address, as it is 3rd person, and formal Sie always is, as it is, functionally, 2nd person.
Even after the spelling reform, this differs slightly from case for pronouns in Russian, and there is no corresponding Russian Ты.
In Italian, lei, loro, voi and even ella can be used as formal forms, and as formal forms of direct address they can be lowercase or letter-case, and so can tu, but in practice the formal forms are usually letter-case, even as clitics, and the informal usually lower.
It seems Spanish usted and ustedes are usually lowercase regardless of politeness, but their abbreviations Ud and Uds are letter-case.