Replacement rear derailleur Recently damaged the rear derailleur on my old city bike - the derailleur is a Shimano integrated 6-7 SIS Max 28t - which is no longer manufactured. I can get a used replacement via ebay but was wondering whether something like a 6/7 speed tourney RD-TY500 would also work. Any thoughts?
Any 6/7 speed Tourney derailleur will be compatible with your shifter, i.e., it will index on a sprocket correctly for each shifter click.

Whatever Tourney model you get you want to make sure it can handle the largest rear sprocket you have and the total capacity which is the difference of tooth counts between smallest and largest sprockets plus  difference of tooth counts between smallest and largest chainrings. Longer cage derailleurs have larger total capacity because they can take up more chain slack.

Specs on the RD-TY500 SGS are here.