Grass Volleyball Shoes
Best ones are often baseball (and some soccer) turf shoes. Soccer ones don't have as much ankle protection or shock absorbing midsoles. The baseball shoes feel a bit more like running shoes than the soccer shoes do. Some trail running (New Balance Arishi V1, etc. have decent traction as well, but usually not as aggressive as these.)
I have Nike Zoom Trouts, some Air Maxes, Adidas Speed Trainer 3, and some older New Balances.
Boombah tends to be a more affordable brand, though you can find clearance or used shoes from the major brands for <$65, sometimes as low as $35 (used).
Nike
Typically "Force Zoom Trout Turf" and "Alpha Huarache Turf" models are good baseball shoes
"Mercurial Superfly TF", "Tiempo TF", "Phantom TF" are good soccer shoes, but probably less
https://www.nike.com/t/force-zoom-trout-ltd-turf-mens-baseball-shoes-rtrDfG/CZ5916-102
https://www.nike.com/t/alpha-huarache-elite-3-turf-baseball-shoes-CQdP8t/CK0748-400
https://www.nike.com/t/mercurial-superfly-8-academy-tf-turf-soccer-shoes-NrdHtk/CV0953-760
https://www.nike.com/t/tiempo-legend-9-club-tf-turf-soccer-shoe-8lrbXd/DA1193-403
https://www.nike.com/t/phantom-gt2-academy-dynamic-fit-tf-turf-soccer-shoe-PDzzf7/DC0802-008
Adidas
https://www.adidas.com/us/adizero-afterburner-turf-shoes/FV9414.html
https://www.adidas.com/us/copa-sense.3-turf-shoes/GW4965.html
https://www.adidas.com/us/predator-freak.3-turf-shoes/FY1038.html
https://www.adidas.com/us/predator-edge.3-turf-shoes/GW9999.html
https://www.adidas.com/us/copa-sense.1-turf-shoes/GW4951.html
New Balance
https://www.newbalance.com/pd/fuelcell-4040-v6-turf-trainer/T4040V6-35599.html
https://www.newbalance.com/pd/fresh-foam-3000-v5-turf-trainer/T3000V5-31210.html
https://www.newbalance.com/pd/fresh-foam-950v3-field/MU950V3-34695.html
https://www.newbalance.com/pd/fresh-foam-950v3-field/MUM950V3-34694.html
Under Armour
Mizuno USA
https://www.mizunousa.com/us/product/softball-mizuno-ambition-as/320595
https://www.mizunousa.com/us/product/baseball-mizuno-dominant-as-mid/320564
https://www.mizunousa.com/us/product/baseball-mizuno-dominant-as-knit/320628
https://www.mizunousa.com/us/product/softball-mizuno-ambition-as-2/320632
Mizuno Japan
Asics Japan
https://www.asics.com/jp/ja-jp/neorevive-tr-2/p/1123A015-008.html?width=STANDARD
https://www.asics.com/jp/ja-jp/ds-light-tf-sl/p/1101A023-001.html?width=WIDE
Boombah
Salomon, Tecnica, and Other Trail Runners
https://www.salomon.com/en-us/shop/sports/trail-running/shoes.html
https://www.amazon.com/s?rh=n%3A7141123011%2Cp_4%3ATecnica&ref=bl_sl_s_sh_web_7141123011
Stores to Check Out
https://www.eastbay.com/category/sport/baseball/mens/shoes.html
https://www.baseballmonkey.com/footwear/mens-footwear/baseball-turf-shoes.html
Some Used Options from Nike
The following aren't all baseball or soccer shoes (some are just training or running) but have aggressive tractions.
Nike Air Max Griffey 2012
Nike Flyposite
Nike Air Max Trainer and Older Models (Pre-2018)