Could someone explain to me how/if this resolves the speed issues that all satellite internet has had since its inception.
When starlink sats are fully using laser interconnects then their long-distance (london-NY or further) latency should be considerably less than anything else available. The speed of light in fibre is about 1/2 the speed of light in a vacuum.
Bandwidth is solved with phased-array antennas at a high carrier frequency (Ku/Ka?). The high carrier frequency allows for high (literal) bandwidth. However, the phased-array antennas are physically the same size as some smaller, lower frequency antennas are, and thus transmit/recieve more power. This stuff in general is called a link budget and is standard in satcom.
Latency is just satellites at a lower orbit. This is only possible now because: 1. Chip manufacturing can produce a cheap phased array antenna that's electronically steered to follow the satellite in low orbit. 2. Launch costs low enough it's economical to launch tons of satellites