How can I cap the total space that mysql / mariadb binary logs take up?
max_binlog_size has little effect on keeping disk space down; expire_logs_days is the one to worry about.

How fast are the logs filling up?

One way binlogs can fill up extremely fast is when you accidentally have the same server_id on multiple servers in a Replication setup.

Which version?  Which binlog_format?  Lots of multi-row UPDATEs/DELETEs?

More

expire_logs_days is the best available builtin tool.  There may be 3rd party monitoring tools (or you could write one) that watch for disk space.

In any system, you should have some kind of monitoring on disk space -- it is not just the binlog that can go berserk.  The "general log" and the slowlog can, also.  And your application can go berserk.  And so forth.