I was checking out a circuit for power management. That's when I came across this unknown component which looks so much like half a transformer and a switch. What exactly is this?
It appears to be a relay, which as you suggest does look a lot like a combination of half a transformer (coil) and a switch; in this case, it is a magnetically operated switch.
Some schematics seem to draw a relay with the extra parallel lines (bars) between the coil and the switch contacts, others do not, so you may not always see those two parallel lines between the coil and switch contacts. To my knowledge this looks like a regular single-throw relay, with a normally open (N/O) switch contact and a normally closed (N/C) switch contact, on either side of the common (usually marked 'C') switch contact.
When the coil is energized by a voltage being applied across it, a magnetic field forms, and this attracts the switch 'arm' away from the N/C switch contact towards the N/O switch contact. When the coil is no longer energized, the switch arm (usually with the aid of an additional spring, spring leaf, or due to the arm being formed from spring steel or similar into a spring-like shape) will return to make contact with the N/C switch contact.
Relays come in many shapes and sizes, some with many series of switch contacts that can be 'thrown' when the coil is energized, and then return to their resting positions after the coil voltage is removed.
Some particularly interesting and complicated relays were used in analogue telephone switch systems, such as these before the advent of fully digital exchanges. Sometimes telephone exchanges will still have some pieces of analogue switch gear working along side the newer digital equipment, but most exchanges are now fully digital. I worked at a British Telecom exchange for a short while in the late 1990's and they were still transitioning from the analogue exchange equipment to a fully digital fibre-exchange, and there were several floors of the building still occupied with huge equipment racks of analogue switch gear and telephone relays. It was quite a sight to behold and to hear!
Wikipedia has some great additional reading on relays too: https://en.wikipedia.org/wiki/Relay
I hope this helps, and hopefully others with more experience than I, will contribute or make corrections if I haven't explained things clearly.
It's a relay. Single-pole double-throw relay, to be precise. Extremely basic and common component. A current through the coil creates a magnetic field to control the switch. Typically used to allow for circuit isolation and/or for using a low current signal to control a high current source. Wiki