Can laotze be considered as one?
LaoTzu is a bodhisattva, likely Equal Enlightenment but has yet to achieve supreme enlightenment as that of Buddha Shakyamuni
U mean he aimed to become a Buddha in future?
All bodhisattva will naturally become Buddha. in bodhisattva, there is no aim, their reincarnation into beings' world are to go through discrimination and attachment of all beings so as to achieve full enlightenment. Some bodhisattva have stronger vow to liberate all beings before attainment and some vow to attain enlightenment before responding to the "sincere demand" of beings to liberate them. As beings heavy, light karmic, affinity and conditions varied, the timeframes on the side of beings to recover back its buddha nature are not equal as well:)
The reign of a buddha of all world systems during same period seems extremely long. With so many aspired to be one, how long will one get their turn?
simply, just in a single mindfulness
In a single mindfulness sounds Savastivada.
Paccekka Buddha is described as one who understands the Truth by his own efforts, but does not obtain omniscience nor mastery over the Fruits or Bodhicitta. Paccekka buddha effort and attainment is also not by chance, it conditioned by his many precious lifespan of practicing enlightenment. Some achieved paccekka buddha triggered from sight of nature like river flowing or leafs falling or hearing of sounds etc. Paccekka buddha and arahat are quite similar, there is a maximum timeframe of their sporadic hibernation in samadhi before entering into bodhisattva learning and attainment prior to supreme enlightenment.