So with obsidian, depending on what you want to do you might not need image representations at all. E.g. obsidian notes are just markdown files, so you could directly export your note to html, pdf, docx, pptx or even images and the equation will automatically get converted into the native format. I often use this method myself to embed equations into teaching slides. They don’t just get converted to images but actual editable pptx equations.
To be able to collect equations together for export you can adopt a number of techniques. You can do pretty much the same thing as you do here. Just add a tag to each equation wherever it occurs and then when you search for the tag it will show you every equation. You can copy and paste the ones that you want to export into an empty note and then export that note to a format of your choice. Obsidian also supports backlinks and transclusions, which are fancy ways of linking and embedding notes into each other. These may offer more ways of achieving what you want to do.
Might I suggest that you give it a try with a few equations and see if works for you? I’m happy to guide you where you get stuck. There’s also a very active obsidian discord community where plenty of people are willing to help.
P.S. obsidian also has a JavaScript based plugin mechanism so if nothing else, you could even write your own plugin to make it do what you want.
