Most users of that era did none of those things. They used apps or shareware they purchased, not much different from today. If anything, it was vastly harder at that time to get the tools to tinker. Compilers and assemblers were quite expensive products; users would be limited to Microsoft GW-BASIC and debug.com that came with MS-DOS or a copy of Borland Turbo Pascal if they were willing to pay extra to get it.
I'm genuinely asking everyone here: How can I do this on a smartphone or tablet? Not just "root it", or install an "alternative OS" that is really just a tweaked Android, and "also you first have to buy this particular device it works on". Preferably without having to solder SMD components.
But from all I've read, I'm expecting the answer is "you can't". Which is too bad, since I have a couple of old devices from family laying around and would like to tinker with them. I'm not connecting them to any network as long as I don't have that level of control over what they do. Wouldn't do it with a new, "secure" device either -- the problem for me is what the built-in software does when working as intended by Goo666le + Shenzhen (I don't trust Apple either, and their devices seem even less hackable).
So if you evaluate it by hardware, it's true that the phone isn't giving the same I/O capability. But the application software is there, there are far more apps for a phone and you can access the old ones in some degree too.
If you need an actually hackable PC equivalent, we have all kinds of boards and configurations, from microcontrollers to rasPi style computers through FPGA boards. Any of them are a tiny fraction of the cost of the old desktops.
These old PCs encouraged exploration, expansion, tinkering, and development. They were true personal devices that you could do whatever you wanted with. Phones are personal in that they know everything about you but they will never match the freedom and exploration of a personal computer.
I truly feel like we've lost something special with the move to smartphones and tablets. :(