God, I'm having flashbacks to an OSHA writeup my spice plant got. We were under SQF 7 at the time which didn't allow for water bottles of any type (no food or drink permitted), OSHA demanding we find a way to allow employees "readily available access to cool water" (because allowing them multiple trips to the breakroom was insufficient), and FDA GMP stating that food or drinks cannot be allowed where food is exposed (which was basically everywhere the OSHA guy demanded employees be permitted to carry water). Lots of back and forth, no Federal effs given for the conflict between FDA and OSHA regs, it was annoying.
In the OP's shoes, I absolutely would not want single use plastics in production or storage. Seems like an easy way to find trash everywhere and catch a finding. If you're offering reusable bottles, I would want to identify/tag them somehow for each employee's use (to help aid when they take them near exposed product which I would never allow), but I'd also add them to a master sanitation schedule for daily just to eliminate the potential for employees to skip washing them. I'd also want to avoid having employees transport them back and forth from the breakroom back to production areas (seems like an auditor would love to ding you for potential allergen contamination). The person who suggested a water cooler with paper cups in a taped off zone is my hero right now lol. Our spice company's solution back in the day was to place a drinking fountain next to the handwash areas when you entered production, we had no complaints from auditors (but we did add it to master sanitation and start swabbing it and the area as part of our routine EMP)