There is a Gimp plug-in called “resynthesizer” which does something similar to content-aware fill. It’s an old plug-in which is minimally maintained and a bit finicky. I installed it yesterday and applied it to that back fence per Richard’s video link, and . . . it was horrible. It looked like Freddy Krueger visited the forest! So with Gimp, I think cloning and healing still gave the best results, scars and all.
Yeah, back when I used Gimp exclusively as my bitmap editor and heard of people with other editors having fancy features like "content-aware fill", I tried the Resynthesizer plugin, but didn't get good results with it. Cloning and healing works best indeed.
When I switched from Linux to a Mac, and Gimp had an issue that rendered it unusable (which is still not fixed, by the way), someone on this forum recommended Affinity Photo to me, and I have used it ever since. The "in-painting brush" works quite nicely, and I used it to "paint away" the fence at the back (along with a "Depth of Field Blur" to mask out imperfections).
The fence at the front was trickier. I tried hiding it completely using dodging and burning layers, but the result wasn't perfect. Therefore I lowered the opacity of those layers, so the fence would still be there, but less prominent than it was before.