How is budget planning evolving for CIOs?

We are trying to increase our allowance for "unplanned" events and re-evaluating our outsourcing in countries outside the USA.  Our over-reliance on more cost effective labor overseas, has bitten us during this Russian War in Ukraine; we had a significant number of staff and developers there, and are now scrambling to transition back to the USA, but the costs of doing so are very high, plus trying to hire the right talent in certain areas is proving to be difficult.
On top of those pressures, we are also trying to consolidate our costs as they relate to The Cloud. It is fairly easy to lose track of what the costs are, especially with elastic computing and ever growing storage needs.

The answer depends on many things such as the industry of business and the type of budget under discussion. In the technology space, IT budgets are growing but being monitored more. There are companies that are more open to experimentation and keep contingency budgets for failures. There are companies that are very agile to market demands and keep aside a lot of headroom to change courses quarterly to quarter. The question is very broad in that sense and the answer differs from company to company

For CIOs budget is always based on the organisation busniess speed. Previous year budget have some impact on the budget planning, as it gives the view on what and where the budget was either under utlized or over utiilzed. As busniess senarios and IT compliances are changing day by day, CIO budget planning is also evolving, now infosecurity  and digital compliances portion have siginificant portion in IT budget. 

IT Budget Planning is one of the Major Task CIO needs to plan without which the IT projects may not roll out smoothly. IT Budget may be categorized in to 2 Broad Categories viz 1. Capex or Capital 2. Opex or Operational. Today majority of Fixed assets falls under Capex Model and all operational recurring subscription expenses falls under OPEX model. So CIO need to Plan it according to above as per organization needs and draft the IT budget for Managements approval with proper justification. In short it is the part of IT projects planning and without which the projects may not get rolled on. Today's trend is to Opt more on Opex model rather going for Capex model as there are many advantages in Opex vs Capex model for example the One Time Down Payment for the Asset in Capex Model is Very High, where as in Opex it is just rental or subscription for desired time period so it is just pay as long as you use it and once discarded then stop paying rental Which makes it feasible and affordable choice. Plus New upgrades and updates are included in subscription model so there is no need of AMC or Administrative expenses. 
So based on your Organizations Needs and priorities and Revenue generation one can plan and spend to increase profitability. However Those assets Which are must for Longer time can be considered under Capex Model.

We have moved to rolling budgets and it makes it so much easier for forecasting and planning each year as you already have the budget ready before you need it. Projects are treated a little differently and managed as a project budget.
I always occasionally review the budget by taking a zero based approach and build up from there to ensure expenses are not continuing to creep up.