Learn Hardcore Turkish: Güvenlik kamerası her şeyi kaydediyor.

The -sı is the 3rd‑person possessive/compound marker used in an indefinite noun compound. Güvenlik kamerası literally means “security camera” (type of camera), formed as Noun1 + Noun2-(s)I. The s is a buffer because kamera ends in a vowel. It doesn’t necessarily mean “its camera” here; it’s the standard way to make compounds like “school bus” (okul otobüsü), “coffee cup” (kahve fincanı), etc.

Why not just say güvenlik kamera?

In Turkish, the typical way to make a noun–noun compound is to add that -(s)I marker to the second noun: güvenlik kamerası. Bare juxtapositions like “güvenlik kamera” are ungrammatical in this meaning.

Does güvenlik kamerası mean “the security camera” or “a security camera”?

Turkish has no articles. Güvenlik kamerası can be “the security camera” or “a security camera” depending on context. If you want to be explicitly indefinite, you can add bir: Bir güvenlik kamerası…

Why is it her şeyi and not her şey?

Because it’s the direct object and it’s specific/total (“everything”), it takes the accusative case: -i. So you get her şey (everything, nominative) → her şeyi (everything, as a specific object).