All the teams you mention are still around @Robbie
Dynamo Dresden never made much of an impact at the very top level, in the last few years they've been jumping between the second and third divisions and have just slipped out of the promotion places in the third division. They're a big club, averaging north of 25,000 at their matches, and take big followings away too. Think Sheffield Wednesday. Dresden is a big city that could easily support a top-flight club if they get their house in order.
Dynamo Berlin (known here as BFC Dynamo) are also still around, but never had much in the way of support as they were the Stasi's favoured club in East Germany. This brought them league titles and European Cup runs back in the day, but now they're stuck in the regional fourth division and play to paltry crowds. Hertha are a different club based in the former West Germany; they played in the Champions League in the recent past but got relegated last season and aren't pulling up any trees this time. They play at the Olympic Stadium in Berlin - they rarely fill it, but are still the capital's best-supported club.
I've been to Cologne's ground before, brilliant experience. Lukas Podolski played for them. They're in the Bundesliga but are struggling right now. This season they sacked their "animated" manager Steffen Baumgart, who then joined Hamburg, a former Bundesliga stalwart that got relegated a few seasons back and keep finding new and amusing ways to not get promoted. Here he is when forced to watch them at home when he was in quarantine.
The finances of football are a bit different due to the rule that club members must have a majority of voting rights in their clubs (with a couple of exceptions), so instead of owners you've got investors and very big sponsors. In the lower leagues, clubs need to apply to the German FA for a licence every season - the FA look at the projected crowds and sponsorship income as well as the planned budget, and can accept it or demand improvements. If no licence is granted, the club is ejected from the league. In the third division, this has led to a situation where none of the teams that finished in the relegation zone were actually relegated - they all got a reprieve as other clubs were expelled instead!