it’s a good feature request, in the mid-time here are some suggestions for your current case
With Typora
Like you said Typora does a good job, perhaps you could try to see if Typora can detect the path of the images used, it might just be a matter of changing the format of obsidian images path to md links instead of wikilinks
This community plugin can help you with that:
https://github.com/agathauy/wikilinks-to-mdlinks-obsidian
that way if things are set up with a relative path in Typora you might be able to easily export from typora.
Other alternatives (With Obsidian)
I still think sharing the markdown file should be the best for a designer to deal with.
In order to do this, just put all the images you are using in a sub folder, if you do it from the obsidian left sidebar (in the file manager) links should update without any issues.
That way you can just send the markdown file with the link of attachments.
It’s all a matter of trying to use MDlinks format for more compatibality for the web designer and more importantly a well organized folder of the images used, that will be really easy for the web designer to deal with.
A new vault (best solution)
If all of this sounds a bit confusing, the easiest solution I would recommend is start a new vault, which contains only what you want the web designer to see and share the whole folder. That’s the easiest solution I can think of.
In my opinion it’s even better than using export to HTML since things are cleaner and easier for a webdesigner to organize the content.
Hope that helps!