None of the type families you mentioned (Arial, Montserrat, Helvetica Neue) were used in the original image. Also, the original raster-based image looks like it was generated via so-called AI. There are strange quirks with the lettering that are common with AI-generated images, such as that strange semicolon. AI doesn't know how to do type very well.
The condensed type looks a lot like Trade Gothic Condensed. Adobe Fonts has a Trade Gothic Next package, but it doesn't look quite the same as Trade Gothic. Latino Gothic Variable might be a decent alternative. The smaller type looks kind of like Gotham with a little bit of Futura or Avenir mixed into it.
Using Illustrator you'll just need to lock down the original image on one layer and build new type objects over the top of it on another layer. Fairly simple process.