My sewing machine is accelerating for an unknown reason

While I don't have this particular machine -

Most of these universal motors use electronic speed controls that use a device called either a TRIAC or SCR, that regulate the motor speed by chopping the mains frequency (i.e. turning on and off rapidly 100 or 120 times per second). The usual failure mode is a short circuit, which will produce the symptoms of "only runs at full speed".
These electronic speed controls also use a filter with capacitors and inductors, and it is possible that a shorted filter capacitor will also produce the same fault, as mentioned in another answer. The capacitors used are known as "X2 class safety capacitors"; they have an internal mechanism that is supposed to clear faults by blowing internal fuses, however this mechanism may not work with low current loads (like sewing machine motors).

This could be caused by a faulty capacitor in the machine.

See glossary item on this website:

Electrical sewing machines have a component inside the motor of the machine called a capacitor. This helps eliminate electrical noise from the motor and prevents the electrical noise from going back into your homes electrical grid. When capacitors age they can split open and leak electrolytical fluid, which renders them faulty. Once this happens, the motor of the machine will at times start running by itself. The best course of action for when this happens is to take it in to get it looked at by a qualified sewing machine technician.

from: https://sewingmachinecentre.nz/pages/glossary#Running-On