There’s really nothing wrong with low side switching of basic loads. If it were something with other connections where that would be a problem, sure, but an led strip or a motor are just fine. You still want high side wiring protection if you’re running those wires through grounded equipment, but that can be the overload protection built in to the power supply in many cases.
That said, you can use N- or P-channel FETs in high-side switching. N-channel typically have lower on resistance and so make more efficient switches, but have the downside of needing a charge pump or similar to provide a gate voltage that’s positive wrt the supply voltage. Fortunately there are ready-made solutions like the one that dobson741 linked.
But it’s worth considering if you really want a FET driver like that. Mostly FET drivers are used to achieve faster switching, which is more efficient, but also more prone to emitting EMI, especially when driving offboard loads with long(ish) wires. You can add filters and other mitigation methods, but simply not switching so fast in the first place can address the problem at the source (

). It’s a bit less efficient, but that can be mitigated by lower PWM frequencies, and isn’t important for an on/off load, as long as you stay within the SOA of the FET.
When using a P-channel FET on the high side, as you’ve noticed, you can’t just pull the gate to ground from 24V. D65 does kinda help that, but going from 24V to 23.3V when abs max is 25V still leaves you way too tight on margin. Remember that absolute maximum ratings are the line beyond which the datasheet and all guarantees about proper function—let alone performance—go out the window. Your design margin needs to be sufficient to absorb supply voltage tolerance/load regulation and any overshoot caused by load path inductance without getting into that territory. Furthermore, to whatever extent that diode helps you limit the max gate voltage, it reduces your ability to turn the gate off, because it limits the ability of the gate driver to pull the gate to the supply voltage to get Vgs to zero. How much of a problem that is depends on the Vgs(th) of the FET and your switching requirements.
A zener on the gate is better, but should be between the gate and source, because the thing you’re trying to limit is the gate-source voltage. Low speed switching can be as simple as a small low-side transistor that pulls the gate/zener cathode towards ground by a suitable resistor.
Simplest solution is still a low-side N-channel FET, though.