I've never found a way to predict what kind of place any given campsite in Germany is, other than laboriously checking each site on the interweb, or zooming in on online maps / satellite photos to see how big the place is.
There's definitely a trend (over the last 20-30 years) towards bigger sites with more facilities, but small, cosy sites with nothing much more than a small toilet block can still be found in both east and west.
Having said that, if you see
Waldcampingplatz in the name (forest campsite) in the East, those are usually quite nice places, with the pitches between trees rather than on a manicured but compacted lawn. Although the Waldcampingplätze can be fairly large, they're quite spread out so don't feel cramped at all.
Personally, I look for
Biwakplatz (bivouaks) and
Wasserwandererrastplatz (water tourist rest spots - for canoers and kayakers). These vary from free to 5€ per head, usually have a picnic bench, toilets (often portaloos) and a water pipe. They can be hard to find (they're marked on waterways maps by Jübermann, see below), or the map on this page has most of the ones I know of personally, so may be fairly comprehensive:
https://trekkingtrails.de/trekkingplaetze/.
This site also includes a lot of the sanctioned Biwaks and Wasserwandererrastplätze, but also many random picnic tables and shelters which are definitely in the category of wild camping:
https://campwild.org/
Finally, I also look up whether I might be passing a
Kanuverein (kayak/canoe club) Clubhaus - they often have space for a tent or two, sometimes have a full campsite (eg an excellent one in Passau). I've spent many pleasant evenings at canoe clubs, drinking beer with the members; they really get the whole bike tour thing. A map of the canoe clubs is here
https://www.kanu.de/DER-DKV/Vereine/Kar ... 52086.html, although you'll need to check the website of each to see whether they have a Clubhaus or land on which you might be able to camp. Again, the Jübermann maps are very helpful here, showing whether a club can accommodate tents along with suggestions for wild camping as well as showing established campsites - but the maps are expensive and only really of use if you're touring on the water or sticking close to the water (cycle routes along the rivers and canals are marked on the newer editions of these maps):
https://www.juebermann.de/shop/category ... erkarten_9. These clubhouses aren't always open - so if you want to be sure they're happy to receive you then phone ahead.
So to summarise: when planning, I first check for bivouaks and Wasserwandererrastplätze, then for a local Kanuverein and only then do I look at 'normal' campsites.
PS sometimes campsites are marked on maps - particularly the kind put up on the roadside by local authorities, but when you get there the site is only for Dauercamper - long term statics.