Apology's just noticed you are on Playstation, just look for the screen with Pilot loadouts/Fighter/SRV/Crew no idea what it looks like on console.
O7
We "look down' to access that menu on consoles (and also I believe on PC) off the top of my head, I think the button combination is Square and down on the d-pad at the same time, on PS4...
So for example, rather than looking left and accessing navigation and missions, looking right and accessing ship systems and looking up and accessing communications, you as said want the down menu that displays and changes role on a ship ...
It's the same place you launch ship launched fighters as well, if your current ship can use them.
Just in case it wasn't said yet, you can't launch an SRV when docked at a ground station or anywhere in the direct vicinity of one, if you're at one, you need to fly at least a 10+ km from one, find a safe and suitable place (basically just large and flat enough for your current ship), to land, then once you've landed you can choose to launch and drive around in an SRV
Also if you drive a set distance from your ship it will fly into orbit to keep it safe (indeed something that is recommended that you do yourself by Dismissing your ship from the down menu if you play in Open), however there's no need to panic when it does so, once you need your ship again, you Recall it from the same menu and it will land itself somewhere safe nearby.
From the same menu you can transfer cargo and board your ship again by driving directly under the SRV hatch (you'll know you're in the right position when you have I think two blue lights on your dashboard).

