I never had 30 elections on one day in Germany (I think 5 was the absolute maximum) as we elect fewer positions in general and don't combine most elections on one day. Usually the federal election is the only vote on that day with some states specifically moving their state election day by one week to avoid a clash. The only usual combination is regional/European elections or state/regional elections for the small states. Referendums (there only a few) are usually tacked onto another election if there is one in a reasonable timeframe.

The elections each use a seperate ballot (and often seperate ballot box) and are counted one after the other with the most important election being counted first while the rest is still locked away in sight.

But yeah, for 30 ballots that system might break down.