my initial thought would be no, JSE shouldn't be used as client support for extensions.
I am not against helping people with Joomla, but I think that it might potentially open a gate that might be very hard to shut later on and trying not to sound elitist I believe such a move would dilute the quality of JSE, particularly in the questions being asked.
I am only new to answering/posting on JSE myself and trying to payback the help I have received by checking the questions most days to see if there is something I can help with. If even only a handful of extensions developers, maybe a few popular ones, offered user support here the volume of questions to trawl through each day would become very time consuming, with more rocks than diamonds creating diminishing returns/benefits. I expect would just go back to using JSE for searching for solutions to my own problems.
The OP gives some indication of why he wants to do this on his support page, https://extensions.schultschik.com/support .
I don't think the original OP is expecting everyone to answer his support requests and the suggestion of using Tags would work well for him, but I can't see any way for me to exclude Tags for extension support questions that I would not be interested in.[Corrected: see comments]
Previous questions specific to an extension and templates that have been asked and the person is referred to contact the developers support site. If this extension support was taken up on JSE then the active individuals would be filtering/moderating posts saying you need to contact the developer or no that developer lives here so you need to Tag it so they will see it. I would rather see the active people like Lodder, Mick, Scholle, FF answering questions not spending their time moderating and redirecting posts.
There would also be the issue of paid support where a customer of an extension developer may not be happy with the quality of support they receive, if it then becomes an issue we all get dragged into it. While we might understand the distinction about where the support is to come from, an angry customer might not and if it is a commercial interest then legal people could be involved. It has got ugly written all over it.
The technical structure of SE doesn't seem to support individual 'vendor spaces' like you could with any number of forum packages that have sub boards.
I can't really see any benefit for JSE, sorry.