There is no specific doc which talks about exact space required for upgrade.
But it is told that enough space should be available. Depending upon type of deployment, whether it is small or, medium or large you can check on space that it need.
Use a medium configuration, or larger, for the master and worker nodes in a vRealize Log Insight cluster. The number of events per second increases linearly with the number of nodes. For example, in a cluster of 3-12 nodes (2 nodes are not supported), the net in a 12 node cluster is 180,000 events per second (EPS) or 2.7 TB of events per day.
By default, the vRealize Log Insight virtual appliance uses the preset values for small configurations, which have 4 vCPUs, 8GB of virtual memory, and 510GB of disk space provisioned. vRealize Log Insight uses 100GB of the disk space to store raw data, index, metadata, and other information.
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/storage/core is where the log buckets are stored, and that is normal to see high utilization (it's expected). The update package does not get stored there and doesn't depend on that space being available, so you should be ok. Keep in mind you have to go through 4.6(.1) before you can go to 4.7. There is no direct 4.5 => 4.7 upgrade. Also, don't forget to snapshot prior to it.