Your included usage resets on the calendar month, not on your account's billing date. Codespaces is a metered product, and GitHub's billing period for metered products runs from 00:00:00 UTC on the 1st to 23:59:59 UTC on the last day of the month. Included compute hours go back to the full amount at the start of each period, and accrued storage goes back to zero. For you that means November 1 at 00:00 UTC.

Your numbers match the cap. GitHub Free includes 120 compute hours a month, and a 2-core machine counts at a multiplier of 2, so 60 hours on a 2-core machine uses the whole allowance.

On the budget questions: a budget only counts paid use, so your included hours never draw it down. A $0 budget with "Stop usage when budget limit is reached" stops usage at the point where you would start paying, and without a payment method on file GitHub blocks overage anyway. After the reset you can resume your existing codespace with the same settings, and you won't be charged.

Two things to watch:

• Storage has its own quota (15 GB-month on Free). A codespace uses storage for as long as it exists, even when stopped, so if you hit that limit you'll be blocked again. Deleting codespaces you don't need stops that storage from adding up.
• If you need your work before the reset, you can still export it while blocked: on github.com/codespaces, open the "..." menu next to the codespace and choose "Export changes to a branch".

Sources:

• Codespaces billing: https://docs.github.com/en/billing/concepts/product-billing/github-codespaces
• Billing cycles: https://docs.github.com/en/billing/concepts/billing-cycles
• Budgets and alerts: https://docs.github.com/en/billing/concepts/budgets-and-alerts