The daily water changes when treating sick fish is about having optimum water quality - it can help limit potential pathogen levels in the aquarium; in treatment tanks (which may be newly set up) it will obviously limit potential ammonia etc re possible non-cycled filter or medication affected filter media
Even a quick daily vacuum of the substrate and various surfaces, can help remove parasite eggs etc
In a planted tank, medication effects may be more variable re possible interaction with plants, substrate etc, which is part of the rationale behind using bare hospital tanks (the bare bottom also allows better observations re fish pooh)
BUT
some fish are very stressed by the minimalist surroundings (obviously light should be dim and good oxygenation of water (eg, filter splashing return, good surface agitation etc; while most air stones will provide additional (gentle) currents, it is not the most efficient manner to oxygenate water) and may have higher survival rates in the planted aquarium
The Manual of Fish Health (Dr. Chris Andrews, Adrian Exell and Dr. Neville Carrington) goes into some detail re water quality, suitable medications/protocols, hospital tank maintenance etc , also directions for preparing medicated food
At this stage, if all fish appear healthy, active, eating - sit quietly and observe the aquarium from a comfortable chair so you can be comfortable with minimal movements for 20-60min - I’d just do daily water changes of 50% (as that’s your normal routine) and monitor the affected fish for improvements: an otherwise healthy fish will show some to significant improvement every day)
The Sera Bactopur Direkt is a good supportive medication (but will not directly impact Columnaris strains)
Praziquantel is relatively effective as a bath (if it’s the appropriate medication) and seems less palatable than levamisol foods (though some of the commercial preps are treated to improve palatability)
Seachem Focus contains a proven compound re preparation of medicated foods: I dissolve the medication, then add Focus (sometimes this does not completely dissolve), then the food (I choose familiar foods that my fish are already excited about eating, allow 10-20min reaction time (this varies with the food and medications)
As Conor mentions it’s not unusual for Corydoras to develop fin “lesions”, and then recover (when otherwise healthy etc) ... though IME these lesions are not “gel-like”
(My experiences with gel-like or seeming “thick bubbles” appearing on fish fins, then fish bodies (as the infection became more systemic) was very negative, feeding levamisol~food offered the best chances of recovery for infected fish. I’ll look for some photos though I’ve lost mine (dead computer) and Pandora’s Box website seems to have disappeared completely (excellent fish disease photos))