Hello VyasaDyda.
and welcome to the Apple (user-to-user) Community!
Re: "Assistance Needed with Apple Vision Pro Setup in ABM" : "I'm trying to manually add the Apple Vision Pro to ABM using Apple Configurator, but I'm not seeing the six-digit code appear on the Vision Pro. I've already tried resetting both the Vision Pro and the Configurator, but it hasn't helped."
Am no expert in this area, yet your question to the community deserves some response.
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Re: "Am I missing something?"
Wondering whether you are signed in to the Apple Vision Pro with the same details you use for ABM:
If the Apple Vision Pro is used for both personal and business accounts:
Apple Support's article below may be helpful:
Account-driven enrollment methods with Apple devices - Apple Support
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For more expert user-to-user communication: Business and Education - Apple Community
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For more expert support from Apple if needed: Business Manager Support Business - Official Apple Support
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Useful Resource: Apple Business Manager User Guide - Apple Support