There is no Photoshop hexagon shape tool, they are created via the polygon tool. Go to the top bar of the application and set the number of sides to 6 for the vector. You can apply the artwork as a layer (vector) as well as a path and also a pixel layer. Hold down the shift to force it to have the flat bottom otherwise you can angle it at any angle. The same tool can be used to create a variety of other vector designs.
You can set the roundness via the top bar. You can change it before you create the artwork. Once you have created it, change the roundness via the properties panel found in the window menu. Apply the design.
It is a live design so you can always modify the roundness via the properties as well as via the live interactive control on the vector itself. Or properties panel. Once you have expanded it then you can longer change it via the properties such as number of sides but it does mean you can manipulate it with the direct selection tool etc.
You don't have to create one of them, you can add multiple designs and then use those via the layers panel and blend and change the opacity and have different colors set such as fills and strokes as well as different styles added to each designs. Either draw a new vector or hold down the alt / option and duplicate the existing one and then re-size etc.
You can always convert the hexagon into a smart object via the layer menu and smart object and convert command and then add adjustments via the image menu as well as add styles as well as adding smart filters and the design is live and the filters applied are live and can be changed at any point You can now add smart filters such as liquify and blurs etc. You don't have to use the polygon too, the pen tool is pretty useful but I think the grid helps here so go to the view menu and show grid and then go to the pen tool and use the layer option.
You don't have to keep the design as is, you can squeeze the vector design, you can use the various pen tools to manipulate the points and shift them such as the direct selection tool. Or use the direct selection tool to manipulate the individual points. There appears to be no auto break the live designs but you can always do it in a number ways such as creating a circle and placing the smaller circle inside and then selecting both and use the layer menu and combine shapes and unite and then use the merge shape components with the control bar for the direct selection tool. With this you can now manipulate all the points on the shape and create all kinds of unique vectors
Even with a single design, you can duplicate it (hold down the alt / opt key and drag) and re-size the artwork (make it smaller) and then align both using the alignment middle center etc and use then go to the layer menu and combine command and use subtract. You now have a more hollow design based on your six sized artwork. Go to the direct selection tool and select all the points and then go to the control bar and use the middle entry and merge components. Hold down the alt / opt key and drag again to duplicate that and you can then create a far more complex design of two hollow artworks and then again with both selected go to the layer menu and combine and use the unite this time. You can use the path selection tool to manipulate the positions of the vectors as they are not fixed until you go to the merge components in the control bar (not sure why that command has never been available in the general menu structure of combine / unite / subtract etc). Once you have used merged, it is now frozen unless you apply an undo.
You can select any of the designs created here and then go to the layers and select one of the bevel, contour, stroke etc. In many of the cases you can add additional strokes to the design as well as add additional shadows etc. You can also convert the style modified vector design via the layer menu and smart object and then you can also combine that with more effects to create a very complex design. You can also select the design and then drag it to the CC library panel found in the window menu and use this artwork in other apps such as Premiere and After Effects as well as in Photoshop. It is also live, you can modify it later if you decide that the glow is wrong or you have the wrong direction