I'm not sure what button the insert picture is (unless it's the quick buttons above the text area where you reply as those are more for media type stuff like outside sources like picture hosting and video sites like YouTube IIRC), but I use the upload a file button (post reply, upload a file, more options are all I got for the three buttons at bottom when typing), then find the TT main folder, then find the tech snap shot (either an old one in the main folder or from the snapshot folder) or the output log in the TerraTechWin64_data folder.
If you are having trouble finding the main folder for TT (as it's inside a LOT of folders (like 5-10 as it's been a while since I had to find it) for me anyways you can right click TT in the steam library, then properties at the bottom of that popup, go to local files tab and click the browse local files which should be the first top most button.
I have a short cut to the steams common folder (all games main folder location) on my desktop so I can find it quicker. You can make one also by the above method for finding TTs main folder and then going up 2 folder (that little up arrow icon on the left of the folder address bar) then making a shortcut to paste on the desktop as for me it does not normally go to the last open/used folder if I exit IE and have to navigate using the quick links on the left side of the explorer window (desktop->common shortcut->TTs folder and so on). Save me a ton of time trying to find the stuff I want to upload on here
I also have a shortcut to the steam picture snapshot (default F12) to upload any pictures I take. Same way as above but used the picture uploader popup windows button when you press the button when in a game and quit.
Hope this helps and let me know if anything was confusing or hard to understand and I will try to clarify it better.
Also keep in mind there is a 1 MB file limit to uploading on here. Tech snapshots are fine as they never really get above 100kb (at least in my experience) but F12 steam pictures can vary in sizes depending on your screen resolution. My resolution is 1176x664 as I have a wide screen pc/tv combo monitor and that was only 1 of 2 that would fit/work and have no trouble uploading those pictures.
The output log as an issue of random bloating above 1 mb (have had it above 330 MB at one time ) so keep an eye on that because you may have to zip it to upload. My experience with it is around 130-150 Mb is the limit of zipping it to compress it to within the forums upload limit. Anything larger than that and you will need to send it via email to them.
Once the dialog box appears requesting an URL it expects the user to provide the direct link to the location of an uploaded photo.
I happen to use imgur.com to upload photos from my computer at which point it creates a photo album entry, on that page with the photo album displaying your uploaded photo I typically right click on the image itself and choose "Open photo in a new tab) which will provide the direct location of the photo in question with a .jpg (usually) extension and copy that address into the dialog box which will typically look similar to this: 'https://i.imgur.com/KmwaaHQ.jpg'
There is also a "preview post" located within more options to ensure that the embedded image displays correctly.