The size of the period and size of the buffer depends on the driver, but if it is the same device, it is likely that the playback and capture devices support the same parameters.
Regardless of whether the settings should be the same, it depends on how your application accesses these devices. As for the driver, these devices work independently.
What buffer / period sizes are used depends on how you want to balance latency, power consumption and overload security. Latency is directly proportional to the size of the buffer on playback devices or the period on capture devices. Energy consumption increases slightly for shorter periods. Xrun's security is enhanced by larger buffers and slightly by shorter periods.
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