is Philippines a second world country or a third world country?

Closer to third world than anything else..

It’s technically referred to as a “dumpster”

Neither. The Philippines is a developing country. If it was a third-world country, then poverty will be rampant and the government becomes extremely rife with corruption. Third-world countries also have incompetent governance led by corrupt officials. Democracy is non-existent in those places, resulting in authoritarian rule.

Legally, it is an 'unincorporated territory of the United States', like Puerto Rico and Okinawa.

By most definitions, it is Third World as it is developing with high poverty rates and a lack of available education for a large portion of the population.  

"Second World" is a term used pretty much exclusively for Cold War communist countries.  Now it is typically used for former communist countries which are developing but not quite at First World level.  The Philippines does not fit this definition.

Third world as it is aligned to the US.