Any long-period discrete analog time-keeping function should be avoided at nearly any cost. Your 15 minute period implies either the baroque complexity of a digital divider chain built out of discrete components i.e. Eccles Jordan bistable (flip-flop) circuits with steering diodes, to get the oscillator frequency up to a more reasonable range, or a RC time constant of approx. 1000 (exact value depends on voltage thresholds. The math says a 1 Meg resistor and a 1000 uF capacitor would do the job, but the math doesn't allow for leakage currents. With a 5v supply, on average the resistor is only going to be passing a couple of uA, but an electrolytic capacitor of that value is likely to be specified to have a max. leakage current of a few tens of uA, so unless you are very lucky and pick a capacitor that's at the extreme low leakage end of the bell-curve, the leakage current will dominate, leading to grossly incorrect timing, or even total failure to reach the end of the timing period.
Also analog timing circuits aren't known for their low power consumption. The quiescent current drawn from the battery by the timing circuit is likely to be greater than the average motor current as it has such a low duty cycle.
Nowadays, even with the supply chain issues, any sane engineer would say "Use a MCU." Even the lowliest 8 pin PIC or AVR, or one of Padauk's sub $0.04 MCUs can do the job with code space and pins to spare. It comes down to availability and cost of development tools. If you don't already have any sort of MCU experience and tools, €5.49 will get you a Digispark Rev 3 clone with an ATtiny85 MCU on it, self-programmable over USB using the Arduino IDE.
Back in the day, before cheap easily reprogrammable MCUs, this would have been a job for 4000 series CMOS logic. The chip of choice would be the
CD4060 (or one of its many second source equivalents) which has an on-chip oscillator suitable for RC timing, crystals and resonators + a 14 stage binary divider chain. To toggle the final output with a 30 minute period, (so it can directly be used to control the H-bridge for a motor wired with diode across its limit switches so it stops at each limit till the drive voltage to it is reversed), would require its oscillator to run at fractionally over 9 Hz, entirely practical for a RC timing circuit with reasonable resistor and capacitor values. Nowadays one might choose the 74HC4060, which is better for 5V and lower supply voltages.
Go back 50 years or so before RCA added the CD4060 to their new 4000 series CMOS product range (launched in 1968), and there was a short window of probably less than a decade when a fairly large board full of transistor flip-flops and logic would have been the preferred solution. Before that, a chain of
Decatron counters dividing down the mains line frequency would have been the preferred electronic implementation, but in nearly all cases an electromechanical solution of a high reduction ratio synchronous gearmotor driving a cam operated switch would have been preferred, because it was far far smaller, cheaper, lower power and more reliable than a chassis full of 30 Decatrons!
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