This is because the budget is only deducted when posting occurs in the accounting module, for example, when creating a vendor bill from a purchase by setting up analytic accounting and posting. This journal entry has not been created when recording the timesheet.

You can use the additional module:

https://apps.odoo.com/apps/modules/18.0/account_budget_timesheet_link

Or after completing the timesheet, create a vendor bill with the quantity according to the timesheet and link it to the analytic account, then post.

Same Problem here, I can't see the amount of timesheets in budgets, just the amount of purchase Orders.