[PeteK]

Okay, here's the update, since I offered before. Looks like it was a leak from the timing chain cover and perhaps the oil pan that resulted in oil being spread around the engine bay. Mechanic seemed legit, said accessory belt would probably have to be replaced too as the oil would have degraded it along with coolant tube (assuming "HOSE RAD OUT" - it was swollen but not at an immediate risk of bursting).

The prices are Canadian (despite "Labor" being spelt the American way hahaha) - Google says 1CAD = 0.74USD right now. A friend (an enthusiast as well, not a mechanic) suggested paying another shop to look at it as well since Toyota's charging ~$2k, just for a peace of mind. Compared to $2k, the $94.61 that Toyota charged to look at it seems to at least be pretty small.

Well, at least this incident can serve as a good learning experience.