Common for vocal octaves to be not exact with written sheet music?

Your example song, "Feeling Good", was first performed in 1964 by Cy Grant in key of B minor. The score you show is in E minor. Michael Bublé sings it in Eb minor. Nina Simone sung it in G minor. The octave in which the melody is sung seems to be a minor detail here.

It is common for singers to transpose the song to match their vocal range.

As I presume, the score you show was written based on Bublé's performance and transposed half step up to make it easier for less experienced instrumentalists to play.

Probably the melody was moved up by an octave to make it easier to read. As @Albrecht Hügli writes, the violin key is the most commonly recognized by most musicians. I rarely see melodies of popular songs written in different keys.

Similarly to "Feeling Good", many songs sung by Frank Sinatra were or became hit songs. They were performed by multiple artists, in various keys, and the sheet music you will find for them can be in any key.

On the contrary, it seems to me songs performed by Bruno Mars or Beyoncé are mostly either original or written for them. They are contemporary popular performers, and their versions of their songs are the most popular (rather than covers), so the popular scores will likely match the performance in more detail.

Well, if a song is notated in G clef it is standard that a male sings one octave below, while a female sings the octave that is written.

So maybe that is what this is about?

I‘ve never cared about this. I think they edit all songs in treble clefs, maybe because pop singers are not all used to read bass or tenor clef.

(Most pop songs for male voices are in a higher range than Bariton while the girls mostly sing lower, say in the same range.)

I was wondering if it's even a thing that sometimes the vocals won't exactly match the sheet music (octave wise), and is it common?

Sheet music of pop songs isn‘t published for singers like classical musicians. It is meant for people who want to have the melody and lyrics and to play it on a keyboard. So most editions are made facilitated and reduced for easier reading and easy playing.