The correct choice would be “She believes in the latest technology”

When referring to a particular technology, you would use the article the.

When referring to technology in general, you would not use an article or the adjective latest in the sentence.

This sentence is referring to a particular technology, not just technology in general, so using the article the is correct. The adjective latest tells us that the sentence is addressing the latest version of a particular technology.

It can be helpful to add more context to see that the technology refers to a particular technology:

She believes in the latest technology from Google.
She believes in the latest technology for electric cars.

If you wanted to express that the subject of the sentence believes in technology in general, then not using the and latest would be correct:

She believes in technology.

The sentence above does not reference any specific technology and can mean any and all technology.

If you want to express that the subject believes in technology in general that was developed recently, you can also phrase the sentence like this:

She believes in modern technology.

This sentence also conveys that the subject believes in modern technology in general but does not refer to any specific technology.

Check out our article The or A/An: A Simple Way to Choose the Right One on more details on how to know whether to use the, a, or an.

The nuances between words like latest and modern can be difficult to catch for a non-native speaker of English. Check out Engram to get instant feedback and suggestions from Engram’s AI-powered technology which will help point you in the right direction for English grammar and naturalness.

AI proofreader | Engram
Write more naturally and get better results with Engram. Engram checks your grammar and suggests more natural English expression.

Reference:

Is “the technology” correct in this sentence or not and why?
This was my statement: “You have to submit to the technology and instead of fighting against its functions try to adapt yourself ... ” Then somebody corrected a part of my sentence to ” . . ...