This work investigates optical spatiotemporal vortices with radial and azimuthal quantum numbers (spatiotemporal Laguerre-Gaussian (STLG) wavepackets). These 3D wavepackets possess phase singularities and edge dislocations, resulting in a multi-ring topology. Unlike conventional spatiotemporal optical vortices, STLG wavepackets carry a composite transverse orbital angular momentum (OAM). Mode conversion between STLG and spatiotemporal Hermite-Gaussian (STHG) wavepackets is demonstrated using spatiotemporal astigmatism. The converted STHG wavepacket's decoupled spatial and temporal intensity enables efficient ultrafast STLG wavepacket recognition. This research offers insights into high-dimensional quantum information, photonic topology, and nonlinear optics, with potential applications in acoustics and electron waves.
