By default, the Optimize Budget tool looks at campaigns that are active at the moment and shows data for them. If there are campaigns that accrued cost earlier in the month but are paused now, their budget won't appear in Optmyzr, being the reason why you'll see a lower number for the actual spend in the tool.
If you select "Show Paused" on the left and update the data, you'll see the total amount spent. This will include the cost accrued by campaigns that are currently paused as well.
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