How do I verify that my hosting provider gave me SSDs?

I searched and found 2 options, none of which I'm confident provided me the answer.

1: cat /sys/block/sda/queue/rotational

This output '1' to stdout. What does this mean?

2: lshw -class disc

but couldn't find anything that answers my question.

Let's try to read 1000 random 4k blocks from first 16GB of a disk:

time for i in `seq 1 1000`; do
    dd bs=4k if=/dev/sda count=1 skip=$(( $RANDOM * 128 )) >/dev/null 2>&1;
done

This is something that should be very slow on rotating drive in comparison with SSD. On my desktop class SSD it ends in about a second. On desktop class 7200rpm rotating drive it ends in 10 seconds.

In a physical machine (not a VPS), you can get the type with smartctl:

smartctl -a /dev/sda

and grep for Rotation:

smartctl -a /dev/sda | grep Rotation
Rotation Rate:    Solid State Device

smartctl -a /dev/sdb | grep Rotation
Rotation Rate:    5400 rpm

It's quite likely you have no chance to identify the disk type inside a VPS, as the hypervisor abstracts the real hardware away from the guest machines.