AdGuard and similar apps such as Blokada function as local VPNs, as mentioned, so most traffic does not pass through any particular external server.
The AdGuard app does use AdGuard's DNS servers, so DNS traffic passes through their servers in Russia: https://community.spiceworks.com/tools/ip-lookup/results?hos...
AdGuard says they do not log DNS queries.
The company was founded in Moscow in 2009. In 2017, they changed their official headquarters to Cyprus: https://adguard.com/en/blog/the-chronicle-of-adguard/amp.htm...