Moving log analytics workspaces to another tenant

I know this is an old question but this may help others who find it.
As usual, there is not 1 "best way" to do it and the value of logs may be limited as resource IDs won't line up in the new tenant. Even so, here is a round up of solutions that should help with a one-off move.

1. Relocate Log Analytics workspace to another region
2. One-time export by using a logic app. See Azure Monitor Logs connector for Logic Apps.
3. One-time export to a local machine by using a PowerShell script. See Invoke-AzOperationalInsightsQueryExport.
4. Schedule export of data based on a log query you define with the Log Analytics query API. Use Azure Data Factory, Azure Functions, or Azure Logic Apps to orchestrate queries in your workspace and export data to a destination. This method is similar to the data export feature, but you can use it to export historical data from your workspace by using filters and aggregation. This method is subject to log query limits and isn't intended for scale. For more information, see Export data from a Log Analytics workspace to a Storage Account by using Logic Apps.
5. Logs Ingestion API in Azure Monitor

For continuous shipping of logs you can use the built-in data export rules in Azure Monitor but the best way is to get the source of the log to send to multiple places before it gets ingested into a single workspace: Log Analytics workspace data export in Azure Monitor