[1] https://www.youtube.com/watch?v=MKC5cdGBY04
[2] https://en.wikipedia.org/wiki/Bitter_Sweet_Symphony#Song_cre...
Occasionally the session players get a credit if they've spent time with the artist co-writing the song.
The difference between making a session contribution and co-writing the song is ambiguous and contested.
As a guide, adding a single instrument line doesn't count as co-writing - not even if the line is so distinctive it effectively makes the song. (This is grossly unfair, but it's how it is.)
A string arrangement doesn't count as co-writing either. Not even if it adds a catchy tune.
Arguing with the performer/producer about chord sequences, lyrics, the main vocal melody, and song structure does count as co-writing. But session musicians who do this are on thin ice if they try it without tacit permission.
tbf the Verve had the 18th best-selling UK album of all time and two other top ten hits off the back of Bittersweet Symphony's airplay, so I think they still ended up in credit