feat(inference): Add BagelNet inference provider documentation

[data-mission]

This PR adds BagelNet as an inference provider following the guidelines in the register-as-a-provider documentation.

Changes:

• Add BagelNet provider template (bagelnet.handlebars)
• Update table of contents (_toctree.yml) with BagelNet in alphabetical order
• Register BagelNet in generate.ts
• Generate BagelNet documentation page

Request Review:

@Wauplin @SBrandeis @julien-c @hanouticelina

Addresses Step 8 of the inference provider registration process.

[SBrandeis]

Hey there!
Thank you for your interest in becoming an Inference Provider and for the excellent work you've put into this integration! We really appreciate the effort.

However, we're currently in a consolidation phase focusing on growing usage of Inference Providers via new features and integrations rather than expanding to new partners. This means we've temporarily paused onboarding new providers while we work on these improvements.

We're not able to provide a specific timeline for when we'll resume new provider onboarding, but we'd love to revisit this integration in the future.
Thanks again for your contribution and understanding!