Visio does support hyperlinks with sub-address:

Here you see dest.vsdx
file with some random shapes and Drawing Explorer open, and source.vsdx
file with single shape that have a text converted to hyperlink with sub-address. Also notice zoom=400
is specified and is respected too.
These files are local on my PC, and it works perfectly.
If I place both files to sharepoint.com site document library and open source.vsdx
in desktop Visio, then the hyperlink works too.
If I open source.vsdx
in Visio Web Access, then hyperlink is https://{something}.sharepoint.com/Documents/dest.vsdx#Page-1/Data?zoom=400
, download is initiated on click, and downloaded file is opened in default view - the bookmark is not working.
I've written a note about fragment locations in Office Documents here on SP.SE, but that was left ignored by original question author. Basic idea is: if browser gets involved, then fragment information is lost, cause it never goes out of the calling application, and Page-1/Data?zoom=400
part never reaches server, and desktop Visio has no idea there was some sub-address.
So we need to know if it's possible to modify the hyperlink to point to address like https://{something}.sharepoint.com/_layouts/15/VisioWebAccess/VisioWebAccess.aspx?id=/Documents/dest.vsdx#Page-1/Data?zoom=400
instead of
https://{something}.sharepoint.com/Documents/dest.vsdx#Page-1/Data?zoom=400
.
Sure it is, but VisioWebAccess.aspx ignores fragment location, and that's a real problem. It opens the diagram, but does not focus/zoom. If that worked out, you could populate a column in SPList with /_layouts/15/VisioWebAccess/VisioWebAccess.aspx?id=/diagram.vsdx#Page/Shape
links and use it to implement that 'click to view a diagram' function.
Maybe you'll manage to somehow reinterpret the idea and find a solution. Then please share.
There is not so much topics & questions on using subaddresses in Visio Web Access in the Internet. Most effective "solution" I've found is from a guy that dumped the idea and used PDF with named destination.