OK, I think you need to install obfs4proxy and then configure your Tor Browser. Here is my configuration in file ~/TorBrowser-Data/torrc:
ClientOnionAuthDir ... ClientTransportPlugin obfs4 exec /usr/local/bin/obfs4proxy DataDirectory ... UseBridges 1 Bridge obfs4 ... Bridge obfs4 ...
Thank you! This works. Though I still wonder why on OpenBSD I need to know how to configure torrc in order to get my bridges to work, where on other os's I could just select built-in ones or paste bridges as normal. Maybe somebody knows why this is the case? Do maintainers on other os's just do additional configuration for their users, but OpenBSD sticks to vanilla experience? Or was it a change to reduce the attack surface for the majority of people who don't live in a country where Tor is blocked?