I can replicate this issue with two simple svgs. I have saved them in Inkscape as "Optimized svg." One with a single path and no end marker, and one with an end marker:
The images show on the Perspective page but the one with a marker does not display in the Image Management window:

Edit: I'm using Ignition Platform 8.1.44
I wouldn't necessarily call that a bug. The SVG standards are monolithic and Ignition supports a fairly large subset of the overall SVG spec but there are definitely things in the SVG spec that don't work in Ignition.
It looks like markers are not supported.
I was able to reproduce the problem you're experiencing. Neither embedded SVGs nor image library SVGs showed the markers. I was able to see the SVG when I used it on a view in Perspective but it showed up with a red X in the image browser. The markers were not shown.
I opened the same SVG in chrome and could see the markers.
You can draw an arrow like you have there without using markers. I would recommend drawing a line with markers and then tracing it with a path line so you get the angles correct. When done, just delete the line with markers so it doesn't show up in the markup.
@Steve_Laubach, thanks. I know there are many things that render in certain browsers and not others. The thing I thought was strange is that the svgs actual render in the designer but not the image manager. I'm guessing the designer is using Chromium or parts of it, just because I've witnessed css that renders in Chrome, Edge, the Designer but NOT in Firefox. I assumed the image manager would be the same. I will avoid using the markers.
The actual Perspective view you're seeing in the Designer is being run by an embedded Chromium rendering engine, but the thumbnail preview you get in image management is being rendered by a much lighter weight pure Java layer, ultimately backed by Apache Batik. It's definitely not a full fledged SVG engine, nor do we intend for it to be used as such, but for a relatively common element I'm surprised it's not loading.
Are there any errors in the designer's "Output Console" window, especially when you bring up image management for the first time?
It's possible this issue will be resolved in 8.3, where some miscellaneous changes were made to the image management tool, but it also wouldn't surprise me if it's still there. You are more than welcome to submit a request to our support department to report this "officially" - even if you just provide your two SVGs, it's a useful point of comparison for us to test against and (eventually, possibly) see about fixing.