They can be made as sturdy and secure as your budget and desire extends. These things would be designed from the ground up to have additional atlas piller supports for redundancy in case a ring gets damaged with many different power supplies to guarantee that the active support system continues to operate.

Remember that you do not need to move all of this mass off anywhere once in place so you build it like a building, not a ship that needs to be optimised for low mass and acceleration.

You do not build these flimsy since even the modest ones will have a big upfront cost and the better equipped one is, the bigger the payoff. They are incredibly easy to extend and maintain once the initial ring is set into place though since they are in orbit so as long as you match its own orbital plane, you can operate on it just fine.

You will have a big superstructure magnetically suspended around the moving ring rotating in the opposite direction to the inner ring at the speed of the earth's own rotation so it stays stationary relative to the ground, and which is both half the reason why we build these things but also makes it significantly difficult to penetrate that inner ring.

That superstructure is going to be much heavier than the inner ring by necessity since that inner ring is moving faster than orbital speeds to counteract the momentum generated by the superstructure. So you might as well use that mass for useful things.

We should also not think of active support structures as somehow less sturdy than passive ones. In fact they are far more sturdy since they can be used to create arbitrarily high levels of compressive strength - whatever level of juice you are willing to expend - and this is where those fusion reactors would indeed come in handy. You would also in reality use multiple inner rings instead of just one though one would be fine too for an initial construction.

Keep in mind though that even considering conventional power sources and no superconductors, these things can regenerate a decent fraction of that expended energy back by using the moving ferromagnetic matter inside to generate electricity through the induction generated by either orbiting along the earth or in the case of the atlas piller, falling all the way down from the mesosphere or even further if you decide that it's worth your investment to extend one all the way to geostationary ala the classic space elevator.

Might be a bit overkill though since the orbital ring itself can easily launch you at decent speeds for cislunar and even interplanetary travel.

You also probably have a shit tonne of solar panels on the superstructure itself and would probably want to add a fission or fusion reactor too for added redundancy since you always want multiple power sources for very large structures.

Either that or we continue to rely on rockets which cannot be scaled up to the point where off world travel is as common as air travel without bringing ecological ruin and gargantuan amounts of noise pollution. It's just about the only real curse of being on a planet that has both a thick atmosphere relative to most rocky planets (in our solar system) and also being the massive of the rocky planets.