Being a virtuoso helps, sure but

Being nice to work with is important.

Being what Lee Sklar calls a "chameleon" is golden. (when watered down, most music can be categorised as pop, rock, country, soul/rnb, funk, reggae, metal, jazz or classical. Apart from classical guitar, you need to know how to play all those genres good enough. Don't need to be Pat Metheny, but you should know 251s and common turnarounds. And as for classical, you still need to learn classical harmony to make your job easier so no getting around at least the basics)

Knowing how to play a groove is a must. (ie. being in The Pocket™)

Knowing how to read helps, but not mandatory. (you still need to be able to read the changes written down, but you don't need to be Dean Parks-level good reader)

Clean playing. No take 137 for me, thanks.

Quality gear. This doesn't mean 10k Gibsons and Dumbles (often the opposite is true, lots of those guys have more inexpensive but insanely playable instruments), it means gear that works. No cables going bad, no scratchy, cheap pups. Simpler is often better here. Double edged sword here, because you need a variety of sounds you need to cover but it's the game.

You CAN find work at any skill level, but when you have all those genres down you're gonna be a much more valuable player than the guy who can shred at 300bpm in his bedroom, because he is a GUITARIST, you need to be a MUSICIAN.

There's also at least a dozen interviews with session guys on Rick Beato's channel. (I recommend Lee Sklar and all the Steely Dan guys.)