How much do you allow technical leads/architects to make certain buying decisions without prior approvals?

It depends on many factors (for example the level of urgency) but usually can be allowed for small expenses.

We had various levels of budget and rules on spending. A lead architect might get approval to spend $10k or even $20k but not if it tied us into a multi year spend. Eg $20k for next 4 years so an $80k commitment not allowed

Oddly once we were acquired by a $50 billion dollar company even senior managers that had hundreds of thousands of signing authority could not order pens and paper. It depends on the control leadership wants both can work